Throughout this paperL denotes a Hopf algebra over the ground field k with a bijective antipode S L, and H denotes a Hopf algebra in the Yetter-Drinfeld category We prove the fundamental theorem for right H-Hopf modules in . We also show that if H is finite dimensional, its k-dual H ^* has a right H-Hopf module structure which is not analogous to usual one. As an application we give a direct proof of the [FMS] result: ifHis finite-dimensional, then it is a Frobenius k-algebra. We also imply the [FMS] description of the dual bases for H