  NGC 1705 is one of the optically brightest and best studied dwarf galaxies.
It appears to be in the late stage of a major starburst and contains a young
super star cluster. Type II supernovae are therefore likely to have been a
major effect in the recent evolution of this galaxy and are likely to have
produced a superbubble whose affects on the low-density ambient interstellar
medium can be ideally studied. ROSAT PSPC observations of this galaxy reveal
two striking blobs of X-ray emission embedded in \Ha loops which can be
interpreted as both sides of the upper plumes of the same superbubble. These
sources are a surprise. They are much softer than those observed from other
starburst dwarf galaxies, and are so soft that they should have been blocked if
the observed Galactic HI column density were uniformly distributed across NGC
1705 or if the sources were embedded in the HI disk of NGC 1705. In addition,
the total X-ray luminosity in the ROSAT energy band of 1.2x10^{38} erg s^{-1}
is low in comparison to similar objects. We discuss possible models for the two
X-ray peaks in NGC 1705 and find that the sources most likely originate from
relatively cool gas of one single superbubble in NGC 1705. The implications of
the exceptional softness of these sources are addressed in terms of intrinsic
properties of NGC 1705 and the nature of the foreground Galactic absorption.
