Solar and stellar flares are powerful events that produce intense radiation across the electromagnetic spectrum. Multiwavelength observations are highly important for understanding the nature of flares, because different flare-related processes reveal themselves in different spectral ranges. To study the correlation between thermal and nonthermal processes in stellar flares, we have searched the databases of Kepler (optical observations) and XMM-Newton (soft X-rays) for the flares observed simultaneously with both instruments; nine distinctive flares (with energies exceeding 10^33^erg) on three stars (of K-M spectral classes) have been found. We have analyzed and compared the flare parameters in the optical and X-ray spectral ranges; we have also compared the obtained results with similar observations of solar flares. Most of the studied stellar flares released more energy in the optical range than in X-rays. In one flare, X-ray emission strongly dominated, which could be caused either by a soft spectrum of energetic electrons or by a near-limb position of this flare. The X-ray flares were typically delayed with respect to and shorter than their optical counterparts, which is partially consistent with the Neupert effect. Using the scaling laws based on the magnetic reconnection theory, we have estimated the characteristic magnetic field strengths in the stellar active regions and the sizes of these active regions as about 25-70G and 250000-500000km, respectively. The observed stellar superflares appear to be scaled-up versions of solar flares, with a similar underlying mechanism and nearly the same characteristic magnetic field values, but with much larger active region sizes.