Abstract: We introduce a class of elliptic PDEs for differential (p,p) forms on compact Kahler manifolds, that generalizes the complex Monge-Ampere equation. We show the existence of smooth solution unique up to addition of constants. For p= n-1, this corresponds to the Monge-Ampere equation for (n-1) plurisubharmonic functions studied by Tosatti-Weinkove. We also study the associated parabolic flow and show convergence in some cases.