  We develop {\em the first analytical theory of multikinks} for strongly {\em
dispersive nonlinear systems}, considering the examples of the weakly discrete
sine-Gordon model and the generalized Frenkel-Kontorova model with a piecewise
parabolic potential. We reveal that there are no $2\pi$-kinks for this model,
but there exist {\em discrete sets} of $2\pi N$-kinks for all N>1. We also show
their bifurcation structure in driven damped systems.
