This paper develops a general method for constructing similar tests based on the conditional distribution of nonpivotal statistics in a simultaneous equations model with normal errors and a known reduced-form covariance matrix. The conditional likelihood ratio test, particularly simple and powerful, is shown to have good power properties, especially when identification is strong. Monte Carlo simulations suggest that this test dominates the Anderson-Rubin test and the score test. When the normality assumption is dropped, approximate conditional tests are found that perform well even with weak identification. The conditional approach is also applied to construct confidence regions centered around the 2SLS and LIML estimators, which have correct coverage probability. The paper includes extensions to models with more than two endogenous variables and discusses the construction of confidence regions.This paper develops a general method for constructing similar tests based on the conditional distribution of nonpivotal statistics in a simultaneous equations model with normal errors and a known reduced-form covariance matrix. The conditional likelihood ratio test, particularly simple and powerful, is shown to have good power properties, especially when identification is strong. Monte Carlo simulations suggest that this test dominates the Anderson-Rubin test and the score test. When the normality assumption is dropped, approximate conditional tests are found that perform well even with weak identification. The conditional approach is also applied to construct confidence regions centered around the 2SLS and LIML estimators, which have correct coverage probability. The paper includes extensions to models with more than two endogenous variables and discusses the construction of confidence regions.