The study considers the ADF and KPSS tests for unit root testing in a time series characterized by a number of structural changes in its mean. Using the Monte Carlo simulation method the percentage points of the tests' distributions are estimated. These two tests are biased towards non-rejection of the unit root. The bias of these tests appears to increase as the number of breaks in the series increases. The overall results in the study indicate that when a time series is subjected to a number of changes, provided the appropriate critical values are used, the unit root tests can erroneously reject the hypothesis of unit root. The tabulated critical values can be used in hypothesis testing.