In my talk, I shall present results that have been obtained in collaboration with Tini Garske, on mutation-selection models which describe the evolution of two- or four-letter sequences. Mutation is modelled as a Markov process, and selection is introduced via a fitness function, which assigns a reproductive fitness to each sequence. We consider permutation-invariand fitness functions, or, more generally, Hopfield-type fitness functions, where the fitness is determined by the overlap with a number of given reference sequences. For infinite sequence length, the equilibrium properties of the sequence space models can be determined from a simple maximum principle, which also proves to be a good approximation for the case of finite sequence length.