Abstract: It is a standard assumption for regression models that the error terms all have equal variances. It is of considerable interest to the test of homogeneity for variance in many practical studies. In this paper, we discuss the test of homogeneity for variance and autocorrelation in linear models with AR（1） errors and random-effects. We study the tests of autocorrelation and heteroscedasticity for random errors and random-effects, respectively. Three test statistics based on the score test are proposed. The simulation study shows that test is good as sample size is large. A practical example is given to illustrate our test method. Our results can also be extended to nonlinear models with AR（1） errors and random effects.