We observed soft X-ray transients; X1608-52 and Cen X-4, in quiescence with ASCA at X-ray luminosities on the order of 10(32-33) erg s(-1). The energy spectra were rather soft for both sources. Blackbody fits to the data required characteristic temperatures of 0.2-0.3 keV and emission regions of similar to 10 km(2). A conspicuous hard tail remained after fitting Cen X-4 with a blackbody curve. An extremely soft spectrum in quiescence seems to be a common property of soft X-ray transients.