  Memory effects are studied in the simplest scalar-tensor theory, the
Brans--Dicke (BD) theory. To this end, we introduce, in BD theory, novel Kundt
spacetimes (without and with gyratonic terms), which serve as backgrounds for
the ensuing analysis on memory. The BD parameter $\omega$ and the scalar field
($\phi$) profile, expectedly, distinguishes between different solutions.
Choosing specific localised forms for the free metric functions $H'(u)$
(related to the wave profile) and $J(u)$ (the gyraton) we obtain displacement
memory effects using both geodesics and geodesic deviation. An interesting and
easy-to-understand exactly solvable case arises when $\omega=-2$ (with $J(u)$
absent) which we discuss in detail. For other $\omega$ (in the presence of $J$
or without), numerically obtained geodesics lead to results on displacement
memory which appear to match qualitatively with those found from a deviation
analysis. Thus, the issue of how memory effects in BD theory may arise and also
differ from their GR counterparts, is now partially addressed, at least
theoretically, within the context of this new class of Kundt geometries.
