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We employed the Very Large Array (VLA) of the National Radio AstronomyObservatory in C configuration to map 39 ultraluminous IRAS galaxies at 6~cmand 20~cm, at resolutions of ~ 4" and 15", respectively, and 24 sources at 6~cmwith in the A configuration with a resolution of ~0.5". Most of the sourceshave radio spectral indices indicative of synchrotron emission (alpha ~ -0.65).There is one source, however, that shows an inverted spectrum with alpha =+2.1; observations at higher frequencies show that the spectrum peaks between 5and 8 GHz, as high as any of the ``gigahertz peaked spectrum'' sources studiedby O'Dea etal. We discuss the implications of this source for observations offluctuations in the CMB.  Two of the sources show multiple unresolved components, another four aredoubles with at least one resolved component, 14 show extended emission whichcould arise from a disk, and two show arc-second long jets. Our data fit thetight correlation found by Helou etal (1985) between far-infrared and microwaveluminosity; this correlation extends to the highest infrared luminosities. Thecorrelation is weaker if only the extended or the nuclear components of theradio luminosity are used. Therefore the far-infrared emission in the majorityof these higher luminosity galaxies is due to the same mechanism as the lowerluminosity FIR sources, which is believed to be star formation, rather thannon-thermal activity in the nucleus. Moreover, the star formation is notconfined to the extended disk in these sources, but is important in the nucleusas well.Comment: In press, Astrophysical Journal. 34 pages, uuencoded gzip'ed  postscript of text, tables and figures. 3 figures not included; contact  Margaret Best at best@ias.edu for hardcopies of thes

VLA Observations of Ultraluminous IRAS Galaxies: Active Nuclei or Starbursts?