We present a theory of spin dynamics caused by spin-orbit coupling for two-dimensional gases of cold atoms and other quasiparticles with pseudospin 1/2 moving in orbital gauge fields. Our approach is based on the gauge transformation in the form of a SU(2) rotation gauging out the spin-orbit coupling. As a result, the analysis of the spin dynamics is reduced to calculation of the density-related susceptibility of the system without spin-orbit coupling at the wavevector determined by the spin-rotation length. This approach allows one to treat the spin dynamics in terms of the linear response theory for bosonic and fermionic ensembles. We study different regimes of irreversible spin relaxation and coherent spin dynamics in these systems. For bosonic gases the effects of low temperature are crucial due to accumulation of particles in the small-momentum subspace even if the Bose - Einstein condensation does not occur due to the system low dimensionality.

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