  We discuss the Bose-Einstein condensation (BEC) for an ideal gas of bosons in
the framework of Tsallis's nonextensive statistical mechanics. We study the
corrections to the standard BEC formulas due to a weak nonextensivity of the
system. In particular, we consider three cases in the D-dimensional space: the
homogeneous gas, the gas in a harmonic trap and the relativistic homogenous
gas. The results show that small deviations from the extensive Bose statistics
produce remarkably large changes in the BEC transition temperature.
