Let (A, (p k)) be a Fréchet Q-algebra with unit e A. The ε− spectrum of an element x in A is defined by σ ε (x) = {λ ∈ C : p k 0 (λe A − x)p k 0 (λe A − x) −1 ≥ 1 ε } for 0 < ε < 1. We show that there is a close relation between the ε−spectrum and almost multiplicative maps. It is also shown that {ϕ(x) : ϕ ∈ M ε alm (A), ϕ(e A) = 1} ⊆ σ ε (x) for every x ∈ A, where M ε alm (A) is the set of all ε− multiplicative maps from A to C