  We study conformal transformations in the most general parity-preserving
models of the New General Relativity type. Then we apply them to analysis of
cosmological perturbations in the (simplest) spatially flat cosmologies. Strong
coupling issues around Minkowski spacetime are seen for many special cases of
these models. At the same time, the behaviour of the most general
three-parameter case seems to be very robust, presumably always with only the
eight first-class constraints coming from diffeomorphisms. Also the case of the
so-called 1-parameter New GR doesn't show any discontinuity between Minkowski
and the cosmology, though without showing any deviations from GR which would be
observable at this level either.
