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In this second part of the paper we discuss TE and TM mode directional couplers made of nonsynchronous, nonidentical asymmetric slab waveguides. Coupling is accomplished with the help of a diffraction grating that is placed on either of the two guides on the side facing the opposite slab. The grating couples the compound modes of the complete slab structure to each other. However, since the two slabs are nonsynchronous, the compound modes resemble closely the modes of each slab in isolation. We also provide approximate expressions that result from approximating the compound modes with the modes of the individual slabs. The accuracy of these approximations is estimated by comparison with the exact results.