  The main result of this paper is the rate of convergence to Hermite-type
distributions in non-central limit theorems. To the best of our knowledge, this
is the first result in the literature on rates of convergence of functionals of
random fields to Hermite-type distributions with ranks greater than 2. The
results were obtained under rather general assumptions on the spectral
densities of random fields. These assumptions are even weaker than in the known
convergence results for the case of Rosenblatt distributions. Additionally,
L\'{e}vy concentration functions for Hermite-type distributions were
investigated.
