  We obtain central limit theorem, local limit theorems and renewal theorems
for stationary processes generated by skew product maps $T(\om,x)=(\te\om,T_\om
x)$ together with a $T$-invariant measure, whose base map $\te$ satisfies
certain topological and mixing conditions and the maps $T_\om$ on the fibers
are certain non-singular distance expanding maps. Our results hold true when
$\te$ is either a sufficiently fast mixing Markov shift or a (non-uniform)
Young tower with at least one periodic point and polynomial tails. %In fact,
our conditions will be satisfied %when $\om$ is the whole orbit the towers. The
proofs are based on the random complex Ruelle-Perron-Frobenius theorem from
\cite{book} applied with appropriate random transfer operators generated by
$T_\om$, together with certain regularity assumptions (as functions of $\om$)
of these operators. Limit theorems for deterministic processes whose
distributions on the fibers are generated by Markov chains with transition
operators satisfying a random version of the Doeblin condition will also be
obtained. The main innovation in this paper is that the results hold true even
though the spectral theory used in \cite{Aimino} does not seem to be
applicable, and the dual of the Koopman operator of $T$ (with respect to the
invariant measure) does not seem to have a spectral gap.
