Under classical assumptions, characterizations are given for two classes of instrumental variable estimators of an equation in a simultaneous system. IV estimators where all instruments are nonstochastic are expressed in terms of multinormal random vectors in exactly the same way as the 2SLS estimator of a just-identified equation. These estimators have no finite moments of positive integral order. The second class, consisting of IV estimators based on certain stochastic instruments, includes the OLS, 2SLS, and modified 2SLS estimators. The inadmissibility (under squared-error loss) of some estimators in this class is considered when the equation being estimated contains two endogenous variables.