For Frechet algebras (A; (p_n)) and (B; (q_n)), a linear map T from A !in to B is almost multiplicative with respect to (p_n) and (q_n), if there exists " epsilon >= 0 such that q_n(Tab - TaTb) <= p_n(a)p_n(b); for all n in N, a; b in A, and it is called weakly almost multiplicative with respect to (p_n) and (q-n), if there exists "epsilon >= 0 such that for every k in N, there exists n(k) in N, satisfying the inequality q_k(Tab - TaT b) <= p_n(k)(a)p_n(k)(b); for all a, b in A. We investigate the automatic continuity of (weakly) almost multiplicative maps between certain classes of Frechet algebras, such as Banach algebras and Frechet Q-algebras. We also obtain some results on the automatic continuity of dense range (weakly) almost multiplicative maps between Frechet algebras.
