We present archival ROSAT data for three recently identified, nearby (D < 70 pc), young ($10-40 Myr) stellar associations: the TW Hydrae association, the Tucana-Horologium association, and the Pictoris moving group. The distributions of ROSAT X-ray hardness ratios (HR1, HR2) for these three groups, whose membership is dominated by low-mass, weak-lined T Tauri stars, are tightly clustered and very similar to one another. The value of HR1 for TW Hya itself-the only bona fide classical T Tauri star in any of the nearby groups-is clearly anomalous among these nearby young stars. We compare the hardness ratio distributions of stars in the three nearby groups with those of T Tauri stars, the Hyades, and main-sequence dwarfs in the field. This comparison demonstrates that the X-ray spectra of F through M stars soften with age and that F and G stars evolve more rapidly in X-ray spectral hardness than do K and M stars. It is as yet unclear whether this trend can be attributed to age-dependent changes in the intrinsic X-ray spectra of stars of type F and later, to a decrease in the column density of circumstellar gas (e.g., in residual protoplanetary disks), or to the diminishing contributions of star-disk interactions to X-ray emission. Regardless, these results demonstrate that analysis of archival ROSAT X-ray spectral data can help both to identify nearby, young associations and to ascertain the X-ray emission properties of members of known associations.