In this paper some methods for testing for the presence of selection at a single locus in a single population are discussed. It is assumed that at that locus only two alleles are present, and that the allele frequencies are observed for a number of generations. Tests are derived for detecting heterozygote advantage, genic selection and more general selection. Some simulation studies illustrate the power, or lack of power, of the tests, and show the connection between on the tests and the theory of Watterson (1979, Advances in Applied Probability 11, 14-30).