We present an ISO SWS and ISOPHOT-S, mid-infrared spectroscopic survey of 15 ultraluminous IRAS galaxies (L(IR)greater than or equal to 10(12) L.). We combine the survey results with a detailed case study, based on arcsecond resolution, near-IR, and millimeter imaging spectroscopy, of one of the sample galaxies (UGC 5101). We compare the near-and mid-IR characteristics of these ultraluminous galaxies to ISO and literature data of 30 starburst and active galactic nuclei (AGN) template galaxies. We find the following: 1. Of the ultraluminous IRAS galaxies in our sample, 70%-80% are predominantly powered by recently formed massive stars, and 20%-30% are powered by a central AGN. These conclusions are based on a new infrared "diagnostic diagram" involving the ratio of high-to low-excitation mid-IR emission lines on the one hand, and the strength of the 7.7 Can PAH feature on the other hand. 2. At least half of the sources probably have simultaneously an active nucleus and starburst activity in a 1-2 kpc diameter circumnuclear disk/ring. 3. The mid-IR emitting regions are highly obscured [A(v)(screen) similar to 5-50 or A(v)(mixed) similar to 50-1000]. In a model where star-forming regions and dense molecular clouds are fully mixed, the ISO-derived, V-band dust extinctions approach the dust column densities inferred from CO millimeter measurements. After correction for these extinctions, we estimate that the star-forming regions in ultraluminous infrared galaxies have ages between 10(7) and 10(8) yr, similar to but somewhat larger than those found in lower luminosity starburst galaxies. 4. In the sample we have studied there is no obvious trend for the AGN component to dominate in the most compact, and thus most advanced mergers. Instead, at any given time during the merger evolution, the time-dependent compression of the circumnuclear interstellar gas, the accretion rate onto the central black hole, and the associated radiation efficiency may determine whether star formation or AGN activity dominates the luminosity of the system.
