  We discuss renormalization group equations (RGE) for the parameters of the
Higgs sector in general Two-Higgs-Doublet Model (2HDM). We present the
three-loop results but consider only contributions due to self-couplings of the
Higgs doublets. We study the structure of RGE and express beta-functions in
terms of reparametrization invariants with respect to higgs-basis rotations.
The Cayley-Hamilton theorem is utilized to reduce both the number of
independent tensor structures in matrix RGE and the number of invariants to a
minimal set. As a by-product of our calculation we discovered that two-loop RGE
of the scalar sector in general QFT with multiple higgses were not properly
implemented in a number of public packages. The latter give rise to a wrong
result when mixing in the scalar sector is allowed.
