  This paper presents Wold-type decomposition for various pairs of twisted
contractions on Hilbert spaces. As a consequence, we obtain Wold-type
decomposition for pairs of doubly twisted isometries and in particular, new and
simple proof of S\l{}o\'{c}inski's theorem for pairs of doubly commuting
isometries are provided. We also achieve an explicit decomposition for pairs of
twisted contractions such that the c.n.u. parts of the contractions are in
$C_{00}$. It is shown that for a pair $(T,V^*)$ of twisted operators with $T$
as a contraction and $V$ as an isometry, there exists a unique (upto unitary
equivalence) pair of doubly twisted isometries on the minimal isometric
dilation space of $T$. As an application, we prove that pairs of twisted
operators consisting of an isometry and a co-isometry are doubly twisted.
Finally, we have given a characterization for pairs of doubly twisted
isometries.
