  We extract the long-distance asymptotic behaviour of two-point correlation
functions in massless quantum integrable models containing multi-species
excitations. For such a purpose, we extend to these models the method of a
large-distance regime re-summation of the form factor expansion of correlation
functions. The key feature of our analysis is a technical hypothesis on the
large-volume behaviour of the form factors of local operators in such models.
We check the validity of this hypothesis on the example of the
$SU(3)$-invariant XXX magnet by means of the determinant representations for
the form factors of local operators in this model. Our approach confirms the
structure of the critical exponents obtained previously for numerous models
solvable by the nested Bethe Ansatz.
