Traditionally, most of the information processing of neural networks is thought to be carried out by excitatory cells. Likewise, recent evidence for temporal coding comes from the study of the detailed firing patterns of excitatory neurons. In the CA1 region of the rat hippocampus, pyramidal cells discharge selectively when the animal is in specific locations in its environment, and exhibit a precise relationship with the ongoing rhythmic activity of the network (phase precession). We demonstrate that during a spatial exploratory behavior on a linear track, inhibitory interneurons also show spatial selectivity and phase precession dynamics. We found that the firing rate of interneurons is modulated reliably up and down around an ongoing baseline activity level for specific locations in the environment, producing robust place-specific increases or decreases in discharge. On some sections of the track, the range of theta phases shifts progressively to earlier parts of the theta cycle as the rat advances, so that a negative correlation between phase and position could be demonstrated. Unlike pyramidal cells, phase and rate were not strongly correlated. We discuss the influence of the intrinsic firing properties of interneurons on a model of phase precession, as well as the influence of the detailed shape of the inhibitory oscillation. These results indicate that spatial selectivity and phase precession in CA1 are not properties restricted to pyramidal cells. Rather, they may be a more general expression of a common interaction between the different inputs impinging on both excitatory and inhibitory cells in CA1 and the intrinsic characteristics of those cells. Furthermore, they suggest that the role of interneurons may extend beyond a global damping of the network by participating in a finely-tuned local processing with the pyramidal cells.