This paper is about colored object programming. It focuses on the rigorous handling of independent supplementary behaviours. Two constructs are elaborated: the first one, termed «mixin", to capture one such behaviour in a well defined and reusable way ; the second one, termed «derivation", to abstract the assembly of a basic behaviour with a mixin one. For the purpose of reusability, specific attachment constraints are specified at the mixin level . A practical proposal is made that enables the specification of mixins to be simplified, without compromising the efficiency of a derivation. In spite of our specific visual formalism (grounded on connectedness), it should be noted that the rigorous proposal made here can be incorporated in state-transition formalisms based on insideness instead of connectedness (i.e. formalisms derived from statecharts)