The behaviour of four adaptive algorithms—LMS, equation error, output error identification and the Goodwin-Ramadge-Caines adaptive control algorithm—are examined in the face of plant parameter variations. The key point to note is that persistency of excitation conditions in the time invariant parameter case guarantees exponential convergence. Then standard and newly developed Lyapunov stability results allow us to guarantee tracking error and parameter error boundedness when the plant parameters are actually time varying.