Delfeayo Marsalis’ many hats include world-class jazz trombonist, record producer, composer, leader of the Uptown Jazz Orchestra, and educator-founder of the award-winning Uptown Music Theatre.

Two of the three musical groups led by Marsalis, the son of pianist Ellis Marsalis and brother of musicians Branford, Wynton and Jason Marsalis, are performing locally this week and next week at Snug Harbor.

The Delfeayo Marsalis Sextet will appear Saturday. The Uptown Jazz Orchestra, which features 14 to 16 players, will play its regular Wednesday night gigs. Marsalis also performs with his quartet and with his father.

Marsalis formed the Uptown Jazz Orchestra in 2008 with fundamental goals in mind.

“The main thing is that it has a certain swing and groove,” he said at his Uptown home. “That groove, that thing that you can’t describe, that’s what people love about New Orleans music.”

After the groove, an eclectic musical reach comes next, Marsalis said.

“The second thing is to be able to play music from the early 1900s to now,” he said. “As far as New Orleans groups performing, it’s the widest range of musical styles in one performance, in one setting.

“We bring together not only the collective sound of New Orleans that we hear emanating from the brass bands and the traditional New Orleans music, but also the modern sound. When the audience is involved, they take that journey.”

The Uptown Jazz Orchestra makes its own arrangements, working from melody only, no sheet music.

“That’s what you see in the New Orleans brass bands,” Marsalis said. “We just bring it into the modern jazz context.”

And the band also stays true to the celebratory spirit of New Orleans music.

“We have a good time, and the audience has a good time,” Marsalis said. “That’s the main intent of the band.”

Having fun on the bandstand doesn’t mean the Uptown Jazz Orchestra and Marsalis’ sextet and quartet aren’t professional. All of them take the stage with a sense of purpose and a professional look.

“We come to work,” Marsalis emphasized. “We’re in suits. A lot of guys in jeans and T-shirts, they don’t really come to work, whereas we want everybody to know we come to take care of business.”

Despite the Uptown Jazz Orchestra’s seven years of existence and the more than 100 recordings Marsalis has produced — for Harry Connick Jr., Terence Blanchard, his brothers Branford and Wynton, father Ellis and many more — he has yet to produce an Uptown Jazz Orchestra album.

“I’ve never been one to overindulge in recordings,” he explained. “To me, when you’re ready to put out the product, then you put it out. We’re finally at that point.”

But getting more than a dozen busy New Orleans musicians together for a recording session is a challenge. “We keep trying,” Marsalis said.

Marsalis’ latest album is “The Last Southern Gentlemen,” his first collaboration with his father, Ellis.

Father and son recorded the album of standards — including “I Cover the Waterfront,” “My Romance,” “Autumn Leaves” and, a different kind of standard, the theme from “Sesame Street” — in Los Angeles.

“We probably should have played more ballads,” Marsalis said. “He’s always wanted me to do a ballad record. I love combining ballads with the lyrical nature of the trombone.”

Marsalis and his father, who turned 80 in November, have taken their “Southern Gentlemen” album on the road. They’ve played about 50 shows, including an appearance last weekend at the 3 Sails Jazz Festival in Toms River, New Jersey.

“He’s the trouper,” Marsalis said of his father. “He’s the cornerstone of the New Orleans music scene. What we (younger musicians) try to play, he’s the only guy in the city who can actually play it.

“The way that my dad plays the piano, it’s as though he’s talking to you. The older musicians sound as though they’re talking to you when they play. I can create the effect with the trombone. That’s the main goal for me when I’m playing, to talk to the audience.

“So, myself, Roderick Paulin, certain musicians — I guess we’re the middle-aged musicians now — it’s our responsibility to continue not only the legacy but also the seriousness and the understanding of jazz that my father has.”