This paper treats the identification and adaptive control of time-varying linear systems. For linear systems with a Gauss-Markov parameter process a global lower bound on the mean square error is obtained which is valid for any causal parameter estimator. A similar lower bound is obtained for any causal, one step-ahead predictor. These bounds are applied to the adaptive control of time-varying systems to obtain a lower bound on closed-loop mean square performance for any causal control law. For a specific control law, mean square stability is established, and through simulations it is seen that the performance nearly meets the theoretical lower bound.