The Japan-U.S. satellite ASCA was launched in February 1993 and provides a new capability to obtain high-resolution X-ray spectra of Wolf-Rayet stars in the 0.5 — 10 keV band. We present spectra of the wide binary HD 193793 (WC7+O4-5) obtained three months after periastron with the WC7 star in front, and of the WN7 star HD 93162 in Carina. The spectrum of HD 193793 is heavily absorbed below 2 keV by the WC7 wind and shows a prominent emission line from He-like iron at 6.7 keV. Acceptable fits were obtained using a Raymond-Smith model with kT ≈ 3 keV and non-solar abundances. In contrast, the spectrum of HD 93162 is softer and shows very little emission above ≍2 keV. The relatively low signal-to-noise precludes emission line analysis, and an acceptable spectral fit was obtained using a simple Bremsstrahlung model with kT ≍ 1.6 keV. No significant variability was detected in the X-ray light-curves of either star.