  Two {\it ASCA} observations were made of two ultra-luminous compact X-ray
sources (ULXs), Source 1 and Source 2, in the spiral galaxy IC 342. In the 1993
observation, Source 2 showed a 0.5--10 keV luminosity of $6 \times 10^{39}$
ergs s$^{-1}$ (assuming a distance of 4.0 Mpc), and a hard power-law spectrum
of photon index $\sim 1.4$. As already reported, Source 1 was $\sim 3$ times
brighter on that occasion, and exhibited a soft spectrum represented by a
multi-color disk model of inner-disk temperature $ \sim 1.8$ keV. The second
observation made in February 2000 revealed that Source 1 had made a transition
into a hard spectral state, while Source 2 into a soft spectral state. The ULXs
are therefore inferred to exhibit two distinct spectral states, and sometimes
make transitions between them. These results significantly reinforce the
scenario which describes ULXs as mass-accreting black holes.
