We present new high resolution (R similar or equal to 21,000) near-infrared (lambda=2 mu m) spectroscopic observations of a sample of flat-spectrum and Class II young stellar objects in the rho Ophiuchi dark cloud. Our observations of the hat-spectrum sources are the first to reveal details about the atmospheres of objects so young that they are still in the protostellar stages of early stellar evolution. The flat-spectrum objects exhibit molecular (GO) and atomic (Na, Sc, Si) line shapes which are consistent with those expected for rotating stellar photospheres. No clear spectroscopic signatures of Line formation in Keplerian circumstellar disks are found. The 2.294 mu m nu=0-2 CO spectra show that the flat-spectrum objects are rotating more rapidly ([upsilon sin i]similar or equal to 26 km s(-1)) than the Class II pre-main-sequence stars in our sample ([upsilon sin i]similar or equal to 12 km s(-1)). Analysis of the relative strengths of the atomic Lines of the two flat-spectrum sources GY21 and VSSG17 indicates that these objects have late spectral types, MO and M2 (or later), respectively. Their surface ,gravities are more similar to those of late-type dwarfs or pre-main-sequence subgiant stars than to those of late-type stellar giants or FU Ori stars. These characteristics can be understood if the absorption lines of flat-spectrum sources arise in stellar (rather than disk) atmospheres that are similar to those of pre-main-sequence subgiant T Tauri stars but are accreting mass from their circumstellar disks at higher rates. (C) 1997 American Astronomical Society.