The present paper deals with the onset of convection in a horizontal layer of a porous material saturated with a viscoelastic nanofluid under the influence of rotation and magnetic field. The momentum equation in porous media was
simulated using the Darcy model. The rheological behavior of viscoelastic nanofluids was described using a Jeffrey
model-type constitutive equation. The viscoelastic nanofluid model contains Brownian motion and thermophoresis effects. The normal mode approach is used in a linear stability study, and the onset criteria for stationary and oscillatory convection are derived analytically. The effects of the Jeffrey parameter, solutal Rayleigh number, medium porosity, nanoparticle Rayleigh number, thermosolutal Lewis number, Chandrasekhar number, Taylor number, Dufour parameter and Soret parameter on the stability of the system were investigated. Stationary and oscillatory convection regimes were calculated and analyzed in detail for various parameters.