  We prove local central limit theorems for partial sums of the form \newline
$\,S_n=\sum_{j=0}^{n-1}f_j\circ T_{j-1}\circ\cdots\circ T_1\circ T_0$ where
$f_j$ are uniformly H\"older functions and $T_j$ are expanding maps. Using a
symbolic representation a similar result follows for maps $T_j$ in a small
$C^1$ neighborhood of an Axiom A map and H\"older continuous functions $f_j$.
All of our results are already new when all maps are the same $T_j=T$ but
observables $(f_j)$ are different. The current paper compliments [43] where
Berry--Esseen theorems are obtained. An important step in the proof is
developing an appropriate reduction theory in the sequential case.
