Quantum field theories with compact non-commutative extra dimensions

We study field theories on spaces with additional compact noncommutative di mensions. As an example, we study phi (3) on R-1,R-3 x T-theta(2) using per turbation theory. The infrared divergences in the non-compact theory give r ise to unusual dynamics for the mode of phi which is constant along the tor us. Correlation functions involving this mode vanish. Moreover, we show tha t the spectrum of Kaluza-Klein excitations can be very different from the a nalogous commuting theory. There is an additional contribution to the Kaluz a-Klein mass formula that resembles the contribution of winding states in s tring theory. We also consider the effect of noncommutativity on the four-d imensional Kaluza-Klein excitations of a six-dimensional gauge field.