A rotating disc galaxy is modelled as a composite system consisting of thin stellar and gaseous discs, which are described by a two-fluid modal formalism. The composite disc system is assumed to retain axisymmetry in the background equilibrium. General density-wave perturbations in the two discs are coupled through the mutual gravitational interaction. We study the basic properties of open and tight spiral density-wave modes in such a composite disc system. Within the Lindblad resonances, perturbation enhancements of surface mass density in stellar and gaseous discs are in phase; this is also true during the initial growth phase of density-wave perturbations. Outside the Lindblad resonances, there exists a possible spiral density-wave branch for which perturbation enhancements of surface mass density in stellar and gaseous discs are out of phase. We discuss implications of these results on the critical parameters for global star formation in barred and normal spiral galaxies and on magnetohydrodynamic density waves within the Lindblad resonances.