Let A be a complex commutative Banach algebra with unit 1 and δ > 0. A linear map φ: A →C is said to be δ-almost multiplicative if |φ(ab) - φ (a) φ (b)| ≤ δ||a|| ||b|| for all a, b ε A. Let 0 < e < 1. The e-condition spectrum of an element a in A is defined by δe.(a) := {λ ε C:||λ-a||||λ- a||-1 ||≥ 1/e} with the convention that ||λ- a|| ||(λ - a)-1|| = ∞ when λ - a is not invertible. We prove the following results connecting these two notions: (1) If φ(1) = 1 and φ is δ-almost multiplicative, then φ(a) ε δe(a) for all a in A.then (2) If φis lenear and φ(a) εδe(a) for all a in A ,then φ-is δ almost multiplicative for some δ. The first result is analogous to the Gelfand theory and the last result is analogous to the classical Gleason-Kahane- Żelazko theorem.