Abstract: We prove that the family of complex differential equations with two monomials, $z' = az^k bar{z}^l + bz^m zbar{z}^n,$ with $k, l, m, n$ nonnegative integers and $a, b in C$, has at most one limit cycle. Moreover, we characterize when it exists and prove that it is hyperbolic. For this family, we also solve the center-focus problem.