In this article, we analyze the existence of the solutions of coupled KdV and BBM equations in a weighted Sobolev space ( wSs-BBM) with initial data u_t- u_xxt-av_xxt+a_1 u_x+a_2 v^p v_x+u^p u_x+a_3 〖(u^p v)〗_x=0 v_t- v_xxt-au_xxt+a_1 v_x+a_2 u^p u_x+v^p v_x+a_3 〖(uv^p)〗_x=0 We use the theory of the semigroups of linear operators and Lax-Milgram lemma for the existence for the Korteweg de Vries equations (wSs-KdV).