Porous nuclear fuel elements for use in advanced high temperature gas-cooled nuclear reactors (HTGR's), and to processes for fabricating them. Advanced uranium bi-carbide, uranium tri-carbide and uranium carbonitride nuclear fuels can be used. These fuels have high melting temperatures, high thermal conductivity, and high resistance to erosion by hot hydrogen gas. Tri-carbide fuels, such as (U,Zr,Nb)C, can be fabricated using chemical vapor infiltration (CVI) to simultaneously deposit each of the three separate carbides, e.g., UC, ZrC, and NbC in a single CVI step. By using CVI, the nuclear fuel may be deposited inside of a highly porous skeletal structure made of, for example, reticulated vitreous carbon foam.