A procedure is described for estimating the rate constants of a two-compartment stochastic model for which the covariance structure over time of the observations is known. The proposed estimation procedure, by incorporating the known (as a function of the parameters to be estimated) covariance structure of the observations, produces regular best asymptotically normal (RBAN) estimators for the parameters. In addition, the construction of approximate confidence intervals and regions for the parameters is made possible by identification of the asymptotic covariance matrix of the estimators. The explicit form of the inverse of the covariance matrix, which is required in the estimation procedure, is presented. The procedure is illustrated by application to real as well as simulated data, and a comparison is made to the widely used nonlinear least squares procedure, which does not account for correlations over time.