The adaptive control of simple linear time-varying systems is treated for the case in which their parameters vary arbitrarily in an unknown compact set. The state variables of these systems are assumed to be available for measurement. It is shown that all the signals in the adaptive system are bounded for any bounded reference input. This result requires neither a modification of the standard adaptive law, nor the persistent excitation of the reference input. The extension of the result to general cases, where only the input and output are accessible, is briefly discussed. >