Carbide combinations of the system Ta-Hf-C are of definite interest in view of their high melting points (e.g. the m.p. of the complex carbide 4TaC times HfC is approximately 3942 degrees centigrade). In this connection the carbide region of this system was investigated with respect to specimens of 51 different alloys whose compositions lie on the sections TaC-HfC and Ta(subscript 2)C-HfC of the constitution diagram. Isothermal sections of this ternary system were accordingly studied by methods of x-ray and metallographic analysis of alloys quenched from 2400 to 1500 degrees centigrade along with measurements of microhardness of these alloys. In all the investigated alloys the melting point did not exceed the melting points of the carbides of tantalum and hafnium, even though it was extremely high(3280-3840 degrees centigrade). A comparison of the isothermal section of the ternary system Ta-Hf-C at 1500 degrees centigrade with its counterpart at 2500 degrees centigrade showed no difference. It is shown that the lattice parameter increases with decrease in its C content and increase in its HfC content. The existence of the complex carbide (ta, Hf)C is established and the region of its homogeneity at high temperatures is defined. The melting point of the eutectic in the system HfC-C is lower (3230 degrees centigrade) than the melting point of the eutectic in the system TaC-C.