Based on the recent progress in the Langlands functoriality for classical groups, we establish the relation between the central value of the Rankin-Selberg L-functions for GL(n) x GL(m) and certain periods of automorphic forms on classical groups. Such a relation is a natural generalization of Gross-Prasad conjecture made about 10 years ago. The lecture is based on the joint work with Ginzburg and Rallis.