SiC-TiC composites have been fabricated by using a mechanochemical processing of a mixture of Si, Ti, and C at room temperature and subsequent hot pressing. TiC powders have been obtained by the mechanochemical processing of a mixture of Ti and C whereas SiC powders has not been obtained from a mixture of Si and C. By using the exothermic reaction between Ti and C, SiC-TiC powder could be obtained from the mixture of Si, Ti, and C using the mechanochemical processing for more than 12h. The X-ray diffraction analysis has shown that the powder subjected to the mechanochemical processing consisted of the particles having crystallite size below 10nm. Fully densified SiC-TiC composites have been obtained by hot-pressing of the powder at 1850$^{C}$ for 3h and it has shown comparable mechanical properties to those of the SiC-TiC composites prepared from the commercially available SiC and TiC powders. Flexural strength of 560 MPa and fracture toughness of 4.8 MP$.$am$\_$1/2/ have been shown for the SiC-TiC composites with composition corresponding to 0.75:0.25:1 mole ratio of Si:Ti:C.