We study in detail the equations of the geodesic deviation in multidimensio
nal theories of Kaluza-Klein type. We show that their 4-dimensional space-t
ime projections are identical with the equations obtained by direct variati
on of the usual geodesic equation in the presence of the Lorentz force, pro
vided that the fifth component of the deviation vector satisfies an extra c
onstraint derived here.