One-dimensional steady-state detonation has been theoretically investigated in a gas with internal degrees of freedom (not directly related to irreversible energy release) characterized by a finite relaxation time r. Relaxing gas is a variant of a system with sound speed dispersion. Detonation in such a system has been studied in detail by Kirkwood and Wood, who have pointed out the difficulties in formulating the Chapman-Jouguet (C-J) condition in such a medium. Self-sustaining (normal) and strong detonations for an arbitrary (Y E r/r, (where ro is the characteristic heat release time) have been determined, using an ideal gas with relaxing vibrational energy of molecules. The "topology" of continuous (in a) evolution of normal and strong detonations in the p-u (pressure and specific volume of gas) plane has been determined with varying (Y. For normal detonations two values (Y* and a** < (Y*, both of the order of unity, have been found to exist such that for the equilibrium c, and frozen ct sound speeds and for gas velocity u relative to the detonation wave at the Jouguet point, we have II = cr if (Y > o*, cr > u > c, if (Y* > (Y > oi**, and u = c, if cx < (Y . The steady detonation wave zone has been matched with the rarefaction wave. The C-J condition has been g*e*neralized and a procedure has been described for calculating the parameters at the Jouguet point and the normal detonation velocity in a real gas mixture with relaxation.