The anisotropic dynamics of spin triplet states (STS) of molecular single crystals in zero constant and weak varying magnetic fields (weakness means the absence of saturation at the steady state and of the nutation at the pulse EPR) directed along the molecular axes, is analytically investigated. The equations are derived for the free motion of the sample magnetization, describing its linear oscillations along that molecular axis, along which its nonzero initial value was created. The tensor of

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... the steady-state dynamical susceptibility to the varying field is found. The result of the action of a short MW pulse on STS is analytically described, containing a periodic dependence on the pulse duration and its detuning. Abovementioned results can be applied also to I=1 NMR, what is important for nitrogencontaining explosives and narcotics monitoring. The anisotropic dynamics of electron spinlattice relaxation (SLR) at its one-phonon mechanism is investigated without the high temperature approximation over the phonon temperature; the SLR rates of the separate transitions of STS are calculated; the corresponding SLR probabilities are written in the form, which supposes the fractal dimensionality d of a lattice; the results with d=4/3 agree well with the experimental data in STS of the buried tryptophan of ribonuclease T1.