We present ROSAT (HRI and PSPC) and ASCA observations of the two luminous (L_x ~10^{41-42} erg s^{-1}) star-forming galaxies NGC3310 and NGC3690. The HRI shows clearly that the sources are extended with the X-ray emission in NGC3690 coming from at least three regions. The combined 0.1-10 keV spectrum of NGC3310 can be described by two components, a Raymond-Smith plasma with temperature kT=0.81^{+0.09}_{-0.12} keV and a hard power-law, Gamma=1.44^{+0.20}_{-0.11}, (or alternatively a harder Raymond-Smith plasma with kT ~15 keV), while there is no substantial excess absorption above the Galactic. The soft component emission is probably due to a super-wind while the nature of the hard emission is more uncertain with likely origins, X-ray binaries, inverse Compton scattering of IR photons, an AGN or a very hot gas component (~10^8 K). The spectrum of NGC3690 is similar, with kT=0.83^{+0.02}_{-0.04} keV and Gamma=1.56^{+0.11}_{-0.11}. We also employ more complicated models such as a multi-temperature thermal plasma, a non-equilibrium ionization code or the addition of a third softer component which improve the fit but not at a statistically significant level (<2sigma). These results are similar to recent results on the archetypal star-forming galaxies M82 and NGC253.
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