We obtain the criterion for local stability against axisymmetric perturbations in gravitationally coupled stars and gas in a galactic disc. The stars and gas are treated as two isothermal fluids, with the random velocity dispersion being higher in stars than in gas. The aim is to obtain a quantitative measure of the mutual destabilizing effect of the two components on each other. The problem is phrased in terms of a complete set of three dimensionless parameters: Q_s and Q_g, the standard Q parameters for local stability for stars alone and gas alone, respectively, and epsilon, the gas mass fraction in the disc. The results for Q_s-g, the two-fluid local stability parameter, and l_s-g, the dimensionless wavelength at which it is hardest to stabilize the two-fluid system, are obtained seminumerically as a function of Q_s, Q_g and epsilon and are presented as contour plots. The Q_s-g values are lower than the one-fluid Q_s or Q_g values, especially for high gas fractions (epsilon>=0.15), indicating that the star-gas disc is more unstable then either constituent fluid by itself. l_s-g shows a bimodal distribution for low gas fractions (epsilon<=0.1) - that is, for low Q_s values l_s-g is in the stellar regime of high wavelengths, and vice versa. In contrast, for high gas fractions (epsilon>=0.15), the variation is smooth. Some applications of these results for the theoretical studies of stability and evolution of galaxies are discussed.