The main purpose of this article is to move the study of dendriform algebras and Rota-Baxter operators to a nonassociative setting beyond the Lie algebras. We show how to associate structures of dendriform type to alternative and exible algebras and characterize the Rota-Baxter op- erators corresponding to them, in order to extend some results that have appeared in the literature for the associative case. These objects are stud- ied in some detail. Also, we show that the usual version of Rota-Baxter operators acts on Leibniz algebras in the same form that they act on Lie algebras and in particular can be used into Leibniz-admissible algebras. As a consequence we arrive to the notion of admissible dendriform al- gebra. Additionally, we propose the concept of generalized dendriform algebra and describe a connection of it with the left-symmetric dialgebras recently introduced by the author.