The periodic homogenization in both space and time of linear as well as nonlinear parabolic differential operators is discussed. Particular attention is paid to the couple of quasilinear monotone operators \(u\mapsto \frac {\partial u}{\partial t}-\text{div}\mathbf {a}(\frac {x}{\varepsilon },\frac {t}{\varepsilon ^{k}},Du)\) \((k=1,2)\) corresponding to a classical case and a somewhat singular case, respectively. A comparative analysis of both cases points out great differences of behaviour arising from the third scale inherent in the case \(k=2\) .