We present the results of a search for variable stars in the Local Group dwarf galaxy Phoenix. Nineteen Cepheids, six candidate long-period variables, one candidate eclipsing binary, and a large number of candidate RR Lyrae stars have been identified. Periods and light curves have been obtained for all the Cepheid variables. Their distribution in the period-luminosity diagram reveals that both anomalous Cepheids (ACs) and short-period classical Cepheids (s-pCC's) are found in our sample. This is the first time that both types of variable stars are identified in the same system even though they likely coexist, but have gone unnoticed so far, in other low-metallicity galaxies such as Leo A and Sextans A. We argue that the conditions for the existence of both types of variable stars in the same galaxy are a low metallicity at all ages and the presence of both young and intermediate-age (or old, depending on the nature of AC) stars. The RR Lyrae candidates trace, together with the well-developed horizontal branch, the existence of an important old population in Phoenix. The different spatial distributions of s-pCC's, ACs, and RR Lyrae variables in the Phoenix field are consistent with the stellar population gradients found in Phoenix, in the sense that the younger population is concentrated in the central part of the galaxy. The gradients in the distribution of the young population within the central part of Phoenix, which seem to indicate a propagation of the recent star formation, are also reflected in the spatial distribution of the s-pCC's.