Abstract. A linear functional T on a Fréchet algebra (A, (pn)) is called almost multiplicative with respect to the sequence (pn), if there exists ε ≥ 0 such that |T ab − T aT b| ≤ εpn(a)pn(b) for all n ∈ N and for every a, b ∈ A.We show that an almost multiplicative linear functional on a Fréchet algebra is either multiplicative or it is continuous, and hence every almost multiplicative linear functional on a functionally continuous Fréchet algebra is continuous.