  We report on the results of the ASCA and ROSAT observations on RX
J0059.2-7138, a transient X-ray pulsar in the Small Magellanic Cloud. The
barycentric pulse period has been precisely determined to be 2.763221 +-
0.000004 s. The pulse shape is almost identical in all of the energy bands. The
pulse fraction increases with the photon energy below ~2 keV, while it is
nearly constant at ~37% above ~2 keV. The X-ray spectrum has been found to
consist of two components. One is dominant above 2 keV, and exhibits sinusoidal
pulsations. This component is well described by a typical model found in many
X-ray binary pulsars, a power-law of photon index 0.4 with an exponential
cut-off at 6.5 keV. The other is dominant below 1 keV and shows no significant
pulsation. This component is represented by either a broken power-law with
photon indices of 2.6 and 5.1 below and above a break energy of 0.9 keV, or a
metal-poor thin-thermal plasma with a temperature of 0.37 keV. The
phase-averaged luminosity is ~1E38 erg s^-1 (0.1-10.0 keV) for both components.
A hint of oxygen over-abundance is found in the absorbing column, possibly due
to circumstellar gas ejected from an evolved companion.
