  We extend our previous results on the number of integers which are values of
some cyclotomic form of degree larger than a given value (see \cite{FW1}), to
more general families of binary forms with integer coefficients. Our main
ingredient is an asymptotic upper bound for the cardinality of the set of
values which are common to two non isomorphic binary forms of degree greater
than $3$. We apply our results to some typical examples of families of binary
forms.
