  Imaging spectroscopy using the new Palomar Integral Field Spectrograph is
presented for the Pa-alpha line in four ultraluminous infrared galaxies. In
most cases, we are able to establish the geometry of the merger, and thus
estimate the time in the merger process at which we are viewing the system. The
resulting range in estimated ages, some of which are very young encounters
(~5x10^7 yr), is not predicted by merger models, which produce high rates of
star formation either 1-2x10^8 years after the first encounter or very late
(~10^9 yr) in the merger process. Even in the very young mergers, the
ultraluminous activity appears to be centrally concentrated on the nucleus of
one of the progenitor galaxies---namely the galaxy with a prograde orbital
geometry. Very high star formation rates (2-5 M_sun/yr) are also observed in
structures believed to be newly formed tidal tails.
  The presence of a significant population of very young ultraluminous mergers,
together with the majority of ultraluminous infrared galaxies existing in the
final stages of merger activity, indicates that the ultraluminous galaxy phase
is at least bimodal in time. An evolutionary scenario is proposed for
ultraluminous infrared galaxies, wherein the far-infrared luminosity may
undergo multiple ultraluminous bursts during the course of the encounter. A
substantial fraction of the merger lifetime may be spent in a phase identified
with the less powerful luminous infrared galaxy class.
