We introduce two new classes of tests for censored data. The first tests for association between survival and a covariate and the second tests for equality of survival distributions between K groups. Both tests are permutation tests based on nonparametric test statistics and, unlike the Wald test in the proportional hazards model or the log rank test, can detect alternatives of the "crossed hazards" type. The tests are simple to implement and require no theoretical analysis by the user nor an appeal to asymptotic distribution theory. Simulation results show that the tests are competitive with their classical counterparts under proportional hazards and superior under certain nonproportional hazards alternatives in both the continuous and K-sample cases. The tests are applied to data from the British Medical Research Council's fourth myelomatosis trial and from a Danish study of malignant melanoma.