This paper presents results on the stability of the wage dispersion model presented in Mortensen (2003). Specifically, four learning processes are tested on a single parameterisation of the underlying model, and the most successful is submitted to a sensitivity analysis. The results illustrate an important problem in evolutionary dynamics first highlighted in Nelson and Winter (1982) - that to play a role in equilibrium, a strategy must be consistent with a previous disequilibrium. The results are ambiguous concerning the applicability of the equilibrium method of Mortensen (2003), as some of the learning processes are stable, whilst others are extremely unstable and exhibit complex dynamics.