We present simultaneous ultraviolet and X-ray observations of the dMe-type flaring stars AT Mic, AU Mic, EV Lac, UV Cet and YZ CMi obtained with the XMM-Newton observatory. During 40 hours of simultaneous observation we identify 13 flares which occurred in both wave bands. For the first time, a correlation between X-ray and ultraviolet flux for stellar flares has been observed. We find power-law relationships between these two wavelength bands for the flare luminosity increase, as well as for flare energies, with power-law exponents between 1 and 2. We also observe a correlation between the ultraviolet flare energy and the X-ray luminosity increase, which is in agreement with the Neupert effect and demonstrates that chromospheric evaporation is taking place.