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The influence of linear, parabolic and inverted parabolic temperature gradients on the onset of double-diffusive Rayleigh-Darcy convection is theoretically investigated. The composite system is constrained horizontally by adiabatic and free-free thermal boundaries, and appropriate interfacial boundary conditions are used to connect fluid-porous layers. The regular perturbation approach is used to determine the critical Rayleigh number expression for different temperature gradients. Graphs are used to investigate the significance of a variety of dimensionless characteristics. The couple stress parameter, couple stress viscosity ratio, solute Rayleigh number, and solute diffusivity ratio clearly have a stabilizing effect on the system, whereas the Darcy number and thermal diffusivity ratio destabilize it. [ABSTRACT FROM AUTHOR]