An incompletely chaotic system, with a perturbation of the integrable part that does not obey selection rules, relaxes to an equilibrium state that lies between the initial state and thermal equilibrium. We analyze here a system of two atoms in a circular transversally harmonic waveguide. The dynamics of expectation values of generic observables and their fluctuations in the long-time limit are studied for this model. The relaxation demonstrates a nonexponential behavior and slows down as the initial-state energy increases. The fluctuation amplitude has a tendency to decrease with an increase of the initial state width.