We present results for two Ultraluminous X-ray Sources (ULXs), IC 342 X-1 and IC 342 X-2, using two epochs of XMM-Newton and NuSTAR observations separated by $sim$7 days. We observe little spectral or flux variability above 1 keV between epochs, with unabsorbed 0.3--30 keV luminosities being $1.04^{+0.08}_{-0.06} times 10^{40}$ erg s$^{-1}$ for IC 342 X-1 and $7.40pm0.20 times 10^{39}$ erg s$^{-1}$ for IC 342 X-2, so that both were observed in a similar, luminous state. Both sources have a high absorbing column in excess of the Galactic value. Neither source has a spectrum consistent with a black hole binary in low/hard state, and both ULXs exhibit strong curvature in their broadband X-ray spectra. This curvature rules out models that invoke a simple reflection-dominated spectrum with a broadened iron line and no cutoff in the illuminating power-law continuum. X-ray spectrum of IC 342 X-1 can be characterized by a soft disk-like black body component at low energies and a cool, optically thick Comptonization continuum at high energies, but unique physical interpretation of the spectral components remains challenging. The broadband spectrum of IC 342 X-2 can be fit by either a hot (3.8 keV) accretion disk, or a Comptonized continuum with no indication of a seed photon population. Although the seed photon component may be masked by soft excess emission unlikely to be associated with the binary system, combined with the high absorption column, it is more plausible that the broadband X-ray emission arises from a simple thin blackbody disk component. Secure identification of the origin of the spectral components in these sources will likely require broadband spectral variability studies.
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