  Making use of a dimensionally-reduced effective theory at high temperature,
we perform a nonperturbative study of the electroweak phase transition in the
Two Higgs Doublet model. We focus on two phenomenologically allowed points in
the parameter space, carrying out dynamical lattice simulations to determine
the equilibrium properties of the transition. We discuss the shortcomings of
conventional perturbative approaches based on the resummed effective potential
- regarding the insufficient handling of infrared resummation but also the need
to account for corrections beyond 1-loop order in the presence of large scalar
couplings - and demonstrate that greater accuracy can be achieved with
perturbative methods within the effective theory. We find that in the presence
of very large scalar couplings, strong phase transitions cannot be reliably
studied with any of the methods.
