  We consider quasi-periodically systems in the presence of dissipation and
study the existence of response solutions, i.e. quasi-periodic solutions with
the same frequency vector as the forcing term. When the dissipation is large
enough and a suitable function involving the forcing has a simple zero,
response solutions are known to exist without assuming any non resonance
condition on the frequency vector. We analyse the case of non-simple zeroes
and, in order to deal with the small divisors problem, we confine ourselves to
two-dimensional frequency vectors, so as to use the properties of continued
fractions. We show that, if the order of the zero is odd (if it is even, in
general no response solution exists), a response solution still exists provided
the inverse of the parameter measuring the dissipation belongs to a set given
by the union of infinite intervals depending on the convergents of the ratio of
the two components of the frequency vector. The intervals may be disjoint and
as a consequence we obtain the existence of response solutions in a set with
"holes". If we want the set to be connected we have to require some
non-resonance condition on the frequency: in fact, we need a condition weaker
than the Bryuno condition usually considered in small divisors problems.
