A new method for the adaptive control of linear systems with time-varying parameters is proposed. The method does not require any restriction on the rates of parameter variations. For linear systems in parametric strict-feedback form a state feedback adaptive backstepping controller with nonlinear damping terms is proposed and stability properties are proved. For systems in observable canonical form an ISS Kreisselmeier filter and an adaptive observer backstepping controller with an additional linear damping term are proposed: these guarantee asymptotic output regulation and bounded states. Simulation results show that the proposed controllers have superior performance over the standard controllers in the presence of varying parameters.