Neuro-Musician is an interactive music composer. It uses neural networks to learn a musical style so that it can play an accompaniment or compose music on its own. After being taught several pairs of input melodies and expected output melodies, Neuro-Musician can play a session with a human musician. Even if the musician plays something unfamiliar, Neuro-Musician responds with a novel and reasonable output. It may even play a completely unexpected phrase that is both novel and exciting. We experimented by having Neuro-Musician play a jam session with a jazz pianist. To compose improvisations, the neural networks had to learn approximately 30 eight-measure patterns.