-------------------------------------------------------------------------- `Renormalization of fermion-flavour mixing' Abstract: I will present an explicit on-shell framework to renormalize the fermion-flavour mixing matrices in and beyond the Standard Model, at one- loop level. The framework is based on a novel procedure to separate the external-leg mixing corrections into gauge-parameter-independent self-mass and gauge-parameter-dependent wave-function renormalization contributions. An important property is that this formulation complies with ultraviolet finiteness and gauge-parameter independence, and also preserves the basic structure of the theory. --------------------------------------------------------------------------