An iterative procedure is given for the estimation of a vector of parameters some of which may be common to more than one of a set of nonlinear regression equations in the model presented. The procedure is given for the situation when the covariance matrix in the model is known and is extended to include the model when the covariance matrix is unknown. The covariance matrix allows for correlation between observations made on different regression equations but for the same value of the independent vector of variables. Under certain assumptions the procedure is shown to converge to a consistent estimator of the vector of parameters with probability one. The procedure is illustrated with data from a compartmental tracer experiment.