Sequential life testing involving the Wald sequential probability ratio test (SPR) has been widely developed for the exponential case. In the present paper the SPR ideas for the exponential case is extended to include testing of hypotheses in which and its alternatives change value a finite number of times during the test. The operating characteristic functions and the average time to termination of the test are derived. Additionally, SPR tests are derived for the normal and Weibull distributions. The OC function and the average time to termination of the test in these cases are approximated by applying the previous results, and assuming that the failure function, (t), of these distributions may be approximated in a finite number of intervals in which the failure rate is constant. Replacement and nonreplacement of items are treated. Two numerical examples illustrate the theory. (Author).