A model of an additive non-Gaussian noise channel with generalized average input energy constraint is considered. The asymptotic channel capacity

, for large signal-to-noise ratio

, is found under certain conditions on the entropy

of the measure induced in function space by the noise process

, relative to the measure induced by

, where is a Gaussian process with the same covariance as that of

. If

and the channel input signal is of dimension

, then

, where

. If the channel input signal is of infinite dimension and

for

, then

.