  Oscillating scalar fields, with an oscillation frequency much greater than
the expansion rate, have been proposed as models for dark energy. We examine
these models, with particular emphasis on the evolution of the ratio of the
oscillation frequency to the expansion rate. We show that this ratio always
increases with time if the dark energy density declines less rapidly than the
background energy density. This allows us to classify oscillating dark energy
models in terms of the epoch at which the oscillation frequency exceeds the
expansion rate, which is effectively the time at which rapid oscillations
begin. There are three basic types of behavior: early oscillation models, in
which oscillations begin during the matter-dominated era, late oscillation
models, in which oscillations begin after scalar-field domination, and
non-oscillating models. We examine a representative set of models (those with
power-law potentials) and determine the parameter range giving acceptable
agreement with the supernova observations. We show that a subset of all three
classes of models can be consistent with the observational data.
