First order conditional rewrite systems R have been extensively studied. If R is confluent and terminating, then narrowing is a sound and complete procedure to compute all solutions of a goal s = t modulo R. Recently there has been developed a satisfactory way to combine higher order terms and unconditional rewriting. In this paper we first show that this approach can be carried over to conditional higher order rewrite systems. Then we study narrowing using higher order rewrite systems. A naive translation of first order narrowing may lead to unsolvable unification problems. So we restrict to ”quasi first order” goals and ”simple” rewrite systems.