For the detection on variance changes in the nonstationary time series with a unit root two types of test statistics are proposed, of which one is based on the cumulative sum of squares and the other is based on the likelihood ratio test. The properties of the cusum type test statistic are derived and the performance of two tests in small samples are compared through Monte Carlo study. It is ovserved that the test based on the cumulative sum of squares can detect a samll change in the variance faster than the one based on the likelihood ratio.