  Within the Closed Time Path (CTP) framework, we derive kinetic equations for
particle distribution functions that describe leptogenesis in the presence of
several lepton flavours. These flavours have different Standard-Model Yukawa
couplings, which induce flavour-sensitive scattering processes and thermal
dispersion relations. Kinetic equilibrium, which is rapidly established and
maintained via gauge interactions, allows to simplify these equations to
kinetic equations for the matrix of lepton charge densities. In performing this
simplification, we notice that the rapid flavour-blind gauge interactions damp
the flavour oscillations of the leptons. Leptogenesis turns out to be in the
parametric regime where the flavour oscillations are overdamped and flavour
decoherence is mainly induced by flavour sensitive scatterings. We solve the
kinetic equations for the lepton number densities numerically and show that
they interpolate between the unflavoured and the fully flavoured regimes within
the intermediate parametric region, where neither of these limits is
applicable.
