We present RXTE observations of LMC X–2 obtained during a five-day interval in 1997 December , during which the source was radiating at a mean intensity near the Eddington limit , and strongly variable on timescales of seconds to hours . The shapes of the X-ray color-color and hardness-intensity diagrams during the observations , the presence of VLFN and HFN in the power spectra , and the high intrinsic X-ray luminosity of LMC X–2 ( which historically spans 0.4–2.0 L _ { Edd } for reasonable estimates of the neutron star mass ) are more characteristic of a Z -source in its flaring branch than of an atoll-source . On this basis , we provisionally reclassify LMC X–2 as a Z -source , the eighth such source known and the first to be detected beyond our Galaxy . Using periodogram and Fourier analysis of the X-ray lightcurve we detect an apparently-significant modulation with a period of 8.160 \pm 0.011 hrs and a semi-amplitude increasing from 14 % in the 1.8–4.0 keV range to 40 % at 8.7–19.7 keV . This X-ray modulation appears to confirm a candidate orbital periodicity determined from optical photometry ten years prior to our campaign , but we can not rule out a chance alignment of intrinsic X-ray flares . Current RXTE ASM light curves and archival EXOSAT observations show no sign of such a pronounced periodicity . The X-ray spectrum of LMC X–2 can be well fit using variations of simple Comptonization models . Fits to phase ( \simeq intensity ) -resolved spectra show strong correlations between the power law slope ( in one parameterization ) or the depth to optical scattering ( in another ) and phase . We discuss the implications of these results for the inclination , geometry , and emitting regions of the LMC X–2 system .