In this chapter an approach to evolutionary programming based upon principles of cultural evolution is developed. In cultural algorithms evolution takes place at two levels: at a micro-evolutionary level, in terms of changes in traits associated with individuals in a population, and at a macro-evolutionary level, in terms of beliefs. In such multiple-inheritance systems there are evolving populations of trait sequences as well as associated belief spaces. The belief spaces are derived from the performance of individual trait sequences and are used to constrain the traits acquired in future populations. There can be changes in the representation of the belief space and in the trait sequences.