  We study the notion of Wach modules in relative setting, generalizing the
arithmetic case. Over an unramified base, for a $p$-adic representation
admitting such structure, we examine the relationship between its relative Wach
module and filtered $(\varphi, \partial)$-module. Moreover, we show that such a
representation is crystalline (in the sense of Brinon), and one can recover its
filtered $(\varphi, \partial)$-module from the relative Wach module.
Conversely, for low Hodge-Tate weights $[0, p-2]$, we construct relative Wach
modules from free relative Fontaine-Laffaille modules (in the sense of
Faltings).
