Despite the obvious role of sharply varying repulsive forces in determining the structure of most liquids, for short periods of time, motion in liquids looks remarkably harmonic. That is, there seem to be well-defined collective, but independent, harmonic modes governing the ultrafast dynamics launched from any given liquid configuration. Because liquids are not truly harmonic, however, these modes cannot last forever. In particular, "instantaneous" modes of this sort eventually have to give way to new instantaneous modes-ones more appropriate to whatever new configuration the liquid has evolved into. In this paper we investigate just this process of mode evolution. By concentrating on solely the highest frequency modes, it is possible to formulate analytical models for both the modes and the anharmonic interactions that affect them. We can therefore begin to understand the mechanisms by which modes change in time and the kinds of time scales on which the specific anharmonic processes occur in liquids. What we find is that there are several rather distinct signatures of anharmonicity : we see first that the anharmonicity within a mode itself continually causes the mode frequency to fluctuate. More sporadically, we find that two different but nearly resonant modes will sometimes interact strongly enough with one another to cause a temporary-though not a permanent-mixing between the modes. Of course, both of these processes are, in some sense, breakdowns of instantaneous-normal-mode theory, but neither of them affects the basic identity and existence of instantaneous modes. The eventual destruction-of the modes turns out to be an even less frequent event precipitated by an even stronger mixing between a mode and the motion of surrounding atoms. It is precisely this longer time scale that may mark the first point at which diffusive motion plays an essential role in liquid dynamics.