A procedure is described for the design of stable adaptive model reference control systems. This procedure combines the Lyapunov method with the use of sensitivity coefficients. A basic algorithm is first obtained and the resulting system is shown to be asymptotically stable in the sense of ‘eventual stability’ as used by La Salle and Rath (1963). Modifications of this algorithm are then proposed which are easier to implement. One of these uses sensitivity coefficients and is studied in some detail.