We study the problem of testing whether a hazard function is monotonic or not. The proposed test statistics, a global test and four localized tests, are all based on normalized spacings. The global test is in fact just the test statistic [Proschan, F. and Pyke, R. (1967). Tests for monotone failure rate. Fifth Berkeley Symposium, 3, 293-313], introduced for testing a constant hazard function versus a nondecreasing nonconstant hazard function. This global test is powerful for detecting global departures of the null hypothesis, but lacks power when there are local departures from the null hypothesis. By localizing the global test, we obtain tests that respond to this drawback. We also show how the testing procedures can be used when dealing with Type II censored data. We evaluate the performance of the test statistics via simulation studies and illustrate them on some data sets.