This paper introduces a conditional likelihood ratio test for structural models, which is a general method for constructing similar tests based on the conditional distribution of nonpivotal statistics in a simultaneous equations model with normal errors and known reduced-form covariance matrix. The test based on the likelihood ratio statistic is particularly simple and has good power properties. When identification is strong, the power curve of this conditional likelihood ratio test is essentially equal to the power envelope for similar tests. Monte Carlo simulations also suggest that this test dominates the Anderson-Rubin test and the score test. Dropping the restrictive assumption of disturbances normally distributed with known covariance matrix, approximate conditional tests are found that behave well in small samples even when identification is weak. The paper develops a general procedure for constructing valid tests of structural coefficients based on the conditional distribution of nonpivotal statistics. When the reduced-form errors are normally distributed with a known covariance matrix, this procedure yields tests that are exactly similar; that is, their null rejection probabilities do not depend on the values of the unknown nuisance parameters. Simple modifications of these tests are shown to be approximately similar even when the errors are nonnormal and the reduced-form covariance matrix is unknown. The conditional approach is employed to find critical value functions for Wald and likelihood ratio tests yielding correct rejection probabilities no matter how weak the instruments. Although the conditional Wald test has relatively poor power in some regions of the parameter space, the conditional likelihood ratio test has overall good power properties. Monte Carlo simulations suggest that this conditional likelihood ratio test not only has power close to the power envelope of similar tests when identification is good but it also dominates the test proposed by Anderson and Rubin (1949) and the score tests proposed by Kleibergen (2000) and Moreira (2001) when identification is weak. The conditional Wald and likelihood ratio tests can also be used to construct confidence regions centered around the 2SLS and LIML estimators, respectively, that have correct coverage probability even when instruments are weak and that are informative when instruments are good. The paper is organized as follows. In Section 2, exact results are developed for the special case of a two-equation model under the assumption that the reduced-form disturbances are normally distributed with known covariance matrix. Sections 3 and 4 extend the results to more realistic cases, although at the cost of introducing some asymptotic approximations. Monte Carlo simulations suggest that these approximations are quite accurate. Section 5 compares the confidence region based on the conditional likelihood ratio test with the confidence region based on a score test that is also approximately similar. Section 6 contains concluding remarks. All proofs are given in the appendix.This paper introduces a conditional likelihood ratio test for structural models, which is a general method for constructing similar tests based on the conditional distribution of nonpivotal statistics in a simultaneous equations model with normal errors and known reduced-form covariance matrix. The test based on the likelihood ratio statistic is particularly simple and has good power properties. When identification is strong, the power curve of this conditional likelihood ratio test is essentially equal to the power envelope for similar tests. Monte Carlo simulations also suggest that this test dominates the Anderson-Rubin test and the score test. Dropping the restrictive assumption of disturbances normally distributed with known covariance matrix, approximate conditional tests are found that behave well in small samples even when identification is weak. The paper develops a general procedure for constructing valid tests of structural coefficients based on the conditional distribution of nonpivotal statistics. When the reduced-form errors are normally distributed with a known covariance matrix, this procedure yields tests that are exactly similar; that is, their null rejection probabilities do not depend on the values of the unknown nuisance parameters. Simple modifications of these tests are shown to be approximately similar even when the errors are nonnormal and the reduced-form covariance matrix is unknown. The conditional approach is employed to find critical value functions for Wald and likelihood ratio tests yielding correct rejection probabilities no matter how weak the instruments. Although the conditional Wald test has relatively poor power in some regions of the parameter space, the conditional likelihood ratio test has overall good power properties. Monte Carlo simulations suggest that this conditional likelihood ratio test not only has power close to the power envelope of similar tests when identification is good but it also dominates the test proposed by Anderson and Rubin (1949) and the score tests proposed by Kleibergen (2000) and Moreira (2001) when identification is weak. The conditional Wald and likelihood ratio tests can also be used to construct confidence regions centered around the 2SLS and LIML estimators, respectively, that have correct coverage probability even when instruments are weak and that are informative when instruments are good. The paper is organized as follows. In Section 2, exact results are developed for the special case of a two-equation model under the assumption that the reduced-form disturbances are normally distributed with known covariance matrix. Sections 3 and 4 extend the results to more realistic cases, although at the cost of introducing some asymptotic approximations. Monte Carlo simulations suggest that these approximations are quite accurate. Section 5 compares the confidence region based on the conditional likelihood ratio test with the confidence region based on a score test that is also approximately similar. Section 6 contains concluding remarks. All proofs are given in the appendix.