www.musicals101.com has some information on Harrigan, Hart, and Braham:

Musical comedy: 1879-1890 (by John Kenrick):

Some British sources suggest that London producer George Edwardes staged the first musical comedies, but most of his Gaiety Theater productions were little more than Gilbert and Sullivan-style operettas with shortened skirts. The form we know as musical comedy was born on Broadway in a series of shows starring Edward (Ned) Harrigan and Tony Hart. Produced between 1878 and 1884, with book and lyrics by Harrigan and music by his father in law David Braham, these musical comedies featured characters and situations taken from the everyday life of New York's lower classes. With these distinctly American works, Harrigan, Hart and Braham laid a path that Broadway musicals would follow profitably for more than a century to come.

Harrigan had made his name as a comedian in the variety melodeons of San Francisco. Hart was a stage-struck reform school escapee with a rare gift for stage comedy. They met the mid-1870s, and soon developed a routine that poked fun at New York's infamous neighborhood militias. These local "guard" troops were little more than uniformed drinking clubs sponsored by local politicians. Weekend parades designed to impress the public were often so beer-soaked that the participants looked ridiculous. To spoof this, Harrigan and Hart donned ill-fitting uniforms and staggered through inept military drills while singing a merry march.

We shouldered arms
And marched
And marched away,
From Baxter Street
We marched to Avenue A.
With drums and fifes
How sweetly they did play
As we marched, marched, marched
In the Mulligan Guards.
- Lyric transcribed from sheet music

Audiences loved the act and the catchy "Mulligan Guard's March" was soon heard all around the world. In the novel Kim, Rudyard Kipling notes that it was a favorite with British troops in India – who replaced the names of New York streets with various Indian locales.

 

The Mulligan Shows
When Harrigan and Hart reached New York, their "Mulligan Guard" act was such a sensation that it played the city's top variety theaters for more than a year. Inspired by this acclaim, the team expanded the act into The Mulligan Guard Picnic (1878), a forty minute sketch that packed audiences into Broadway's Theatre Comique for a month -- a very healthy commercial run for that time. This became the first in a seven year series of full length musical farces. The versatile Harrigan performed, produced, and directed while writing the scripts and lyrics. The action was always set on the scruffy streets of downtown Manhattan, with Harrigan playing politically ambitious Irish saloon owner "Dan Mulligan" and Hart winning praise as the African American washerwoman "Rebecca Allup."

The Mulligan Guard Ball (1879), Cordelia's Aspirations (1883) and the rest of the series proved extremely popular with New York's immigrant-based lower and middle classes, who loved seeing themselves depicted on stage. Powerful politicians made a point of showing up too, anxious to curry the favor of voters. Harrigan & Hart's plots focused on such real-life problems as interracial tensions, political corruption and gang violence, but there was always enough clownish humor to keep everyone laughing. Since every class and ethnic group was treated as fair game (and often depicted with surprising sympathy), nobody took offense. 

Harrigan's dialogue relied on puns and ethnic dialect to win laughs. In Squatter Sovereignty (1882), an Irish immigrant has the following exchange with his wife when he realizes a fish has been tied to his back as an April Fool's prank –

MICHAEL: Be heavens, that's a haddock.
ELLEN: 'Tis, and was hanging to a sucker.
MICHAEL: You're only codding me.
ELLEN: What eels you?
MICHAEL: I've smelt that before.

Harrigan and Braham's songs were in the popular style of their day, with lots of sentiment and street-smart humor. The lyrics were redolent with slang, ethnic accents and imperfect grammar, speech forms which had not been set to music before. New Yorkers adored these tunes, and every neighborhood in Manhattan rang with renditions of "Paddy Duffy's Cart" or "The Babies on Our Block" –

If you want for information
Or in need of merriment,
Come over with me socially
To Murphy's tenement.
He owns a row of houses
In the first ward, near the dock,
Where Ireland's represented
By the babies on our block.
There's the Phalens and the Whalens
From the sweet Dunochadee,
They are sitting on the railings
With their children on their knee,
All gossiping and talking
With their neighbors in a flock,
Singing "Little Sally Waters"
With the babies on our block.
"Oh, little Sally Waters,
Sitting in the sun,
A-crying and weeping for a young man;
Oh rise, Sally, rise,
Wipe your eye out with your frock";
That's sung by the babies
A-living on our block.
- Lyric transcribed from sheet music

Since these songs were only peripherally connected to the plots of the shows, hits from previous scores could be interpolated when things needed a lift. Harrigan and Hart could always find an excuse to reprise their "Mulligan Guards March," to show-stopping effect.

Harrigan's penchant for hiring relatives annoyed Hart, who's wife felt he was being slighted. The team split up in 1885. Hart went off on his own, but the crippling effects of advanced syphilis forced him off the stage in 1886, and he died soon afterwards at age 36. Harrigan continued to produce and star in musicals until 1893. George M. Cohan's jaunty "H-A-double R-I-G-A-N spells Harrigan" was an affectionate tribute to this early giant of the American musical stage.

Noteworthy sources on Harrigan & Hart:
Kahn, E.J. The Merry Partners: The Age and Stage of Harrigan and Hart. (New York: Random House, 1955)

Moody, Richard. Ned Harrigan - From Corlear's Hook to Herald Square. (Chicago: Nelson Hall, 1980)

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Harrigan, Edward (Ned)
Actor, singer, librettist, lyricist, producer
b. Oct. 26, 1844 (New York City) - d. June 6, 1911 (New York City)
Beginning as a comedian in touring variety shows, Harrigan eventually teamed with Tony Hart – a young comic with a flair for female impersonation. After their "Mulligan Guards" sketch made them variety stars, the team developed a series of songs and sketches featuring lower class characters drawn from the streets of New York. In time, these sketches evolved into seventeen full length farcical musical comedies that delighted Broadway audiences from 1878 to 1885.

Harrigan ultimately wrote the the book and lyrics for more than twenty five Broadway musicals, including The Mulligan Guards' Ball (1879) and Cordelia's Aspirations (1883), all with melodies composed by father in law David Braham. Harrigan's nepotistic habit of hiring relatives eventually drove Hart to discontinue the partnership. Harrigan continued writing and performing until 1893. One of the most beloved theatrical figures of his time, he was the inspiration for George M. Cohan's hit song "Harrigan" ("H, A, Double-R, I, G-A-N spells Harrigan!")

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Hart, Tony
(b. Anthony J. Cannon)
Actor, singer, producer
b. July 25, 1855 (Worcester, Mass) - d. Nov. 4, 1891 (Worcester)
Hart escaped a reform school to start a career touring in variety. He soon teamed up with Edward Harrigan, and the duo won acclaim with slapstick skits, most notably one in which they sang of "The Mulligan Guards." This grew into a series of farcical musical comedies that focused on the experiences of lower class immigrant New Yorkers. Hart was noted for his extraordinary ability to portray women, especially the comic blackface role of "Rebecca Allup" in several of the "Mulligan" shows.

Hart's drag performances were so accurate that some questioned his sexual orientation, and his marriage did little to quell the rumors. When Hart's wife encouraged him to feel professionally and personally slighted by Harrigan's nepotistic hiring practices, Hart ended the partnership and tried starring on his own. Advanced syphilis (Victorians called this horrifying condition "paresis") soon forced him off the stage, leading him to madness and death at age 36.