  We prove that a wide class of models of Markov neighbor-dependent
substitution processes on the integer line is solvable. This class contains
some models of nucleotide substitutions recently introduced and studied
empirically by molecular biologists. We show that the polynucleotide
frequencies at equilibrium solve explicit finite-size linear systems. Finally,
the dynamics of the process and the distribution at equilibrium exhibit some
stringent, rather unexpected, independence properties. For example, nucleotide
sites at distance at least three evolve independently, and the sites, if
encoded as purines and pyrimidines, evolve independently.
