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The structural, elastic, magnetic and electronic properties of titanium-based alloys TiX2 (X = Cr, Mn) are investigated by the first-principles calculations based on density functional theory using the Vienna ab-initio simulation code. The lattice constants of TiX2 (X = Cr, Mn) alloys are optimized for various possible structures such as hexagonal, tetragonal and orthorhombic. TiX2 (X = Cr, Mn) alloys are highly stable in hexagonal structure with the space group P63/mmc at ambient pressure. A pressure-induced structural phase transition from hexagonal structure to the tetragonal structure is observed in TiCr2 at 443.3 GPa and in TiMn2 hexagonal structure to orthorhombic structure is at 295.05 GPa. The electronic structure shows that TiX2 (X = Cr, Mn) alloys are metallic in nature at all pressures. The magnetic property of nonmagnetic TiX2 (X = Cr, Mn) alloys are analyzed by doping with ferromagnetic materials (Fe, Co and Ni) using the stoichiometries of TiX 2 − z Y z (X = Cr, Mn; Y = Fe, Co and Ni; z = 0.5,1,1.5). It is seen that the magnetic moment is induced by the substitution of ferromagnetic materials with TiX2 alloys. [ABSTRACT FROM AUTHOR]