The high pressure preparation of superconducting thorium sesquicarbide permitted its use as a matrix whereby the effects of the addition of incremental quantities of rare-earth elements on the transition temperature could be studied. Thorium -rare-earth carbide superconducting solid solutions of general formula (Th, R.E.) 2C 3 ( R. E. Ho, Er, Lu as well as Sc) have been synthesized under conditions of high pressure and high temperature. Transition temperatures of 4.1 to 11.7 K were observed and are dependent upon the rare-earth element and the thorium/rare-earth atomic ratio. The occurrence of superconductivity in these systems is limited by the thermodynamic stability of the superconducting phase and the conversion from the superconducting state to one of paramagnetism. Light rare-earth elements such as Ce, Pr, and Nd also form superconducting solid solutions but with depressed transition temperatures. The intermediate rare-earth elements Gd, Tb and Dy form magnetic solid solutions at the concentration levels investigated. The (Th,R.E.) 2C 3 solid solutions crystallize in the body-centered cubic Pu 2C 3 ( D5 c ) structure.