"Alfons Maria Mucha (1860 – 1939), known in English as Alphonse Mucha, was a Czech Art Nouveau painter and decorative artist, known best for his distinct style. He produced many paintings, illustrations, advertisements, postcards, and designs."
Doesn't say much, does it?
People mention Eugene-Samuel Grasset as one of his influences. I'm pretty sure he was influenced by everything around him, just like everyone else, but Grasset isn't bad.
Other influences mentioned are Hans Makart
The Five Senses
Jules Joseph Lefebvre
I mean... *leer*
Japanese woodcuts - the great wave of Japonisme that flushed over Europe in the end of the 19th century.
Here's a long list of different Art Nouveau poster artists and others, that might be of interest. There's a lot Muchaesque things there - it's difficult to know who influenced whom ;-)