  We investigate the fully general class of non-expanding, non-twisting and
shear-free D-dimensional geometries using the invariant form of geodesic
deviation equation which describes the relative motion of free test particles.
We show that the local effect of such gravitational fields on the particles
basically consists of isotropic motion caused by the cosmological constant
Lambda, Newtonian-type tidal deformations typical for spacetimes of algebraic
type D or II, longitudinal motion characteristic for spacetimes of type III,
and type N purely transverse effects of exact gravitational waves with D(D-3)/2
polarizations. We explicitly discuss the canonical forms of the geodesic
deviation motion in all algebraically special subtypes of the Kundt family for
which the optically privileged direction is a multiple Weyl aligned null
direction (WAND), namely D(a), D(b), D(c), D(d), III(a), III(b), IIIi, IIi,
II(a), II(b), II(c) and II(d). We demonstrate that the key invariant quantities
determining these algebraic types and subtypes also directly determine the
specific local motion of test particles, and are thus measurable by
gravitational detectors. As an example, we analyze an interesting class of type
N or II gravitational waves which propagate on backgrounds of type O or D,
including Minkowski, Bertotti-Robinson, Nariai and Plebanski-Hacyan universes.
