For 0 < ε < 1, the ε-condition spectrum of an element a in a complex unital Banach algebra A is defined as, (Formula Presented). This is a generalization of the idea of spectrum introduced in [5]. This is expected to be useful in dealing with operator equations. In this paper we prove a mapping theorem for condition spectrum, extending an earlier result in [5]. Let f be an analytic function in an open set Ω containing σε(a). We study the relations between the sets σε(f(a)) and f(σε (a)). In general these two sets are different. We define functions φ(ε), ψ (ε) (that take small values for small values of ε) and prove that f(σε(a)) ⊆ σφ(ε)(f(a)) and σε(f(a)) ⊆ f(σ ψ(ε)(a)). The classical Spectral Mapping Theorem is shown as a special case of this result. We give estimates for these functions in some special cases and finally illustrate the results by numerical computations. © 2014 Springer Basel.