Electronic, structural and thermodynamic properties of the equiatomic alloyTiZr are calculated within the electron density functional theory and theDebye–Grüneisen model. The calculated values of the lattice parametersa andc/a agree well with the experimental data for theα,ω andβ phases. Theω phaseis shown to be stable at atmospheric pressure and low temperatures; it remains energetically preferableup to T = 600 K. The α phase of the TiZr alloy becomes stable in the range600 K < T < 900 K, and theβ phase attemperatures above 900 K. The constructed phase diagram qualitatively agrees with the experimentaldata available. The tendency toward decomposition in the equiatomic alloyω-TiZr is studied. It is shown that in the ground state theω phase of the ordered equiatomic alloy TiZr exhibits a tendency toward ordering, ratherthan decomposition.