This work treats the analysis of two adaptive systems described by error models. The desired but unknown parameters of each adaptive system are, however, not independent. In general, only linear constraints upon these parameters are considered, although a constant but unknown scalar that introduces some nonlinearities is acceptable within the given constraint. The necessity of this analysis frequently arises, in the areas of both adaptive control and parameter estimation. It is shown that, if the relationship between ideal parameters is linear, it is then possible to find coupled adaptive laws such that the overall adaptive system is globally stable for each type of known error model. Simulations show that the parameter estimation is generally much closer using coupled adaptive laws than those not incorporating the information contained within the constraint.