A numerical study is made of the linearized spin-up process of a double-diffusive fluid in a vertically mounted cylindrical vessel of aspect ratio 0(1). Both the temperature and concentration conditions render gravitationally stable contributions to the overall density profile. Numerical solutions are acquired to the time-dependent axisymmetric Navier-Stokes equations, using the standard Boussinesq fluid approximations. The major nondimensional parameters are identified. Results are compiled for small Ekman number, the Prandtl number similar to 0(1), and broad ranges of the stratification number St, buoyancy ratio R-p, and Lewis number Le, are dealt with. The evolution of the azimuthal velocities is described, and the attendant meridional flows are depicted. The global spin-up process is retarded for a double-diffusive fluid, and this trend is more pronounced as R-p increases. The spatial nonuniformity of the rate of spin-up is enhanced as St and R-p increase. The effects of double-diffusion on the fields of perturbation density, temperature, and concentration are plotted. The impact of Le on spin-up is illustrated, and the plots of the perturbation physical variables of interest are presented. (C) 1997 by Elsevier Science Inc.