A theory for strongly coupled waveguides is discussed and applied to two- and three-waveguide couplers and optical wavelength filters. This theory makes use of an exact analytical relation governing the coupling coefficients and the overlap integrals. It removes almost all of the constraints imposed by a simpler and approximate coupled-mode theory by Marcatili. It also satisfies the energy conservation and the reciprocity theorem self-consistently. We show very good numerical results with the overlap integral as large as 49 percent. The applications to electrooptical modulators, power dividers, power transfer devices, and optical filters are all presented with numerical results.