  In this article we extend the effective field theory framework describing new
physics effects to the case where the underlying low-energy theory is a
Two-Higgs-Doublet model. We derive a complete set of independent operators up
to dimension six assuming a $Z_2$-invariant CP-conserving Higgs potential. The
effects on Higgs and gauge boson masses, mixing angles in the Higgs sector as
well as couplings to fermions and gauge bosons are computed. At variance with
the case of a single Higgs doublet, we find that pair production of SM-like
Higgses, arising through dimension-six operators, is not fixed by
fermion-fermion-Higgs couplings and can therefore be sizable.
