Spin dynamics of two-dimensional electron gas confined in an asymmetrical quantum well is studied theoretically in the regime where the scattering frequency is comparable with the spin precession frequency due to the conduction band spin splitting. The spin polarization is shown to demonstrate quantum beats. If the spin splitting is determined by both bulk and structural asymmetry mechanisms the beats are damped at zero temperature even in the absence of a scattering. We calculate the decay of spin beats due to the thermal broadening of the electron distribution function and electron scattering. The magnetic field applied along the structure growth axis is shown to increase the frequency of the beats and shift system towards the collision dominated regime. ; Comment: 6 pages, 2 figures