The potential discrepancies between the anomalous magnetic moments of the electron and the muon and their Standard Model expectations are addressed in the context of a class of Two Higgs doublets models with tree level neutral flavour conservation. These ``anomalies'' can be explained in two regimes, either scalar masses $>1.3$ TeV and similar vacuum expectation values of the scalar doublets, or scalar masses $<1$ TeV and a strong hierarchy of vacuum expectation values. The electron anomaly is explained through two loops contributions in both regimes; the muon anomaly is explained through two loops contributions for large scalar masses, and through one loop contributions in the second regime with scalar masses $<1$ TeV.