  We prove the existence of local constancy phenomena for reductions in a
general prime power setting of two-dimensional irreducible crystalline
representations. Up to twist, these representations depend on two parameters: a
trace $a_p$ and a weight $k$. We find an (explicit) local constancy result with
respect to $a_p$ using Fontaine's theory of $(\varphi, \Gamma)$-modules and its
crystalline refinement due to Berger via Wach modules and their continuity
properties. The local constancy result with respect to $k$ (for $a_p\not=0$)
will follow from a local study of Colmez's rigid analytic space parametrizing
trianguline representations. This work extends some results of Berger obtained
in the semi-simple residual case.
