  After the recent discovery of a Higgs-like boson particle at the CERN
LHC-collider, it becomes more necessary than ever to prepare ourselves for
identifying its standard or non-standard nature. The Electroweak parameter
Delta r relating the values of the gauge boson masses [MW,MZ] and the Fermi
constant [G_F] is the traditional observable encoding high precision
information of the electroweak physics at the quantum level. In this work we
present a complete quantitative study of Delta r in the framework of the
general (unconstrained) Two-Higgs-Doublet Model (2HDM). First of all we report
on a systematic analysis of Delta r at the full one loop level in the general
2HDM, which to our knowledge was missing in the literature. Thereby we extract
a theoretical prediction for the mass of the W-boson in this model, taking MZ,
\alpha_{em} and G_F as experimental inputs. We find typical corrections leading
to mass shifts $\delta MW \sim 20-40 MeV$ which help to improve the agreement
with the experimentally measured value, in a degree no less significant than in
the MSSM case. In the second part of our study we extend our calculation beyond
the mere one-loop order. We devise an effective Lagrangian approach that
captures the dominant higher order quantum effects on delta rho (viz. that part
of Delta r describing the breaking of the approximate SU(2) custodial symmetry)
in the limit of large Higgs boson self-interactions. This limit constitutes a
telltale property of the general 2HDM which is unmatched by e.g. the MSSM. Our
conclusion is that the Electroweak precision program to be conducted at the
LHC, and maybe at a future linear collider, can nicely complement the direct
searches. Should these distinctive loop effects be eventually found they would
signal a smoking gun hinting at non-standard Higgs physics.
