The purpose of the present paper is to try to find an answer to the question: how are complex signs analyzed in English morphology in the context of Axiomatic Functionalist Theory? The paper provides the tools for analyzing items like hatless, penniless, lioness, countess, hooliganism, and Marxism which are traditionally recognized as morphologically complex, each consisting of two morphemes: a free morpheme and a bound morpheme. With an eye to the notions sign and complex sign as envisaged in Axiomatic Functionalist Linguistics three of these items namely, penniless, countess and Marxism turn out to be unanalyzable, i.e. pseudo-composite
