In this talk we will explain the period relations for critical values of Rankin-Selberg L-functions for the case of GL(n)×GL(n-1), which is an automorphic analog of Deligne's conjecture. The main novelty is a proof of archimedean period relations, which is based on an explicit comparison between Rankin-Selberg integrals and the integrals over the open orbit of certain spherical variety. It is a joint work with Jian-Shu Li and Binyong Sun