This paper deals with single-equation estimators in a simultaneous system of linear stochastic equations and approximates the distribution function of the two-stage least-squares estimators up to terms whose order of magnitude is 1/@?N, where N is the sample size. For fixed N, an approximation to the OLS distribution function is also obtained up to terms whose order of magnitude 1/@m, where @m2 is what is referred to in the literature as the concentration parameter.