  The R\'enyi and Tsallis entropies are discussed as possible alternatives to
the Bekenstein-Hawking area-law entropy. It is pointed out how replacing the
entropy notion, but not the Hawking temperature and the thermodynamical energy
may render the whole black hole thermodynamics inconsistent. The possibility to
relate the R\'enyi and Tsallis entropies with the quantum gravity corrected
Bekenstein-Hawking entropy is discussed.
