We investigated the structural, elastic and electronic properties of 4d-transition-metal carbides (ZrC, NbC) and nitrides (ZrN, NbN) and their ternary alloys ZrxNb1-xC and ZrxNb1-xN in the range 0≤x≤1 by using the APW+lo method to solve Kohn-Sham equations. We have used the local density approximation for the exchange and correlation potential. The ground state properties, equilibrium lattice constants, bulk moduli, elastic constants, densities of electron states and band structures are determined and discussed for all compounds and their related ternary alloys. The results are compared to calculations performed for the similar systems and with experiments. A model structure of 16-atoms supercell is used. {\textcopyright} 2009 Elsevier B.V. All rights reserved.