Introductions of nonindigenous species can have significant effects. It is commonly claimed that the rate of species introductions to the United States has increased over time. This claim is based in part on the increasing rate of discoveries of introduced species. This discovery rate is influenced by factors other than the introduction rate. These include the sampling rate and population growth in the introduced species. In this article, we show that the discovery rate can increase even when there is no increase in either the introduction rate or the sampling rate. This suggests that the basis for some claims regarding an increasing rate of introductions may be invalid.