We present a theoretical and experimental study of ``low-frequency'' magnetic resonance. We show that the usual theory fails to correctly describe magnetic resonance, at frequencies of the order of the linewidth or smaller than the linewidth, in anisotropic systems. Bloch equations must be generalized in order to include two damping terms: one in the oscillating field polarization direction, and the other in the direction perpendicular both to the oscillating field and to the static field. These damping terms may be very different from each other.In particular, we focus on the case of a linear chain of spins with exchange and dipolar interactions, for which the damping is zero in the chain direction: Signal enhancement and line shift arise, especially when the oscillating field polarization axis is parallel to the chain axis, and such effects are strongly dependent to the polarization orientation. A microscopic theory based on the memory-function formalism which describes the polarization is fully given in this paper. It takes into account all nondiagonal terms of the frequency-dependent susceptibility tensor. For the linear chain it turns out that there is a perfect correspondence between phenomenologic theory and microscopic theory for two preferred orientations of the static field: parallel and perpendicular to the chain axis. This means that the relaxation of a total spin component can be considered as exponential for these orientations, with respective rates 1/${T}_{2c}$=0 and 1/${T}_{2t}$. We consider also the real case by taking into account phenomenologically interchain interactions (1/${T}_{2c}$\ensuremath{\ne}0). Experiments have been performed on the quasi-one-dimensional compound (${\mathrm{CH}}_{3}$${)}_{4}$${\mathrm{NMnCl}}_{3}$ (TMMC), using a homemade spectrometer, at frequencies ranging between 25 and 225 MHz. All expected effects have been verified and we deduce the low-frequency--low-field damping 1/${T}_{2c}$=5\ifmmode\times\else\texttimes\fi{}${10}^{8}$ rad ${\mathrm{s}}^{\mathrm{\ensuremath{-}}1}$ and 1/${T}_{2t}$${=10}^{10}$ rad ${\mathrm{s}}^{\mathrm{\ensuremath{-}}1}$. For all field orientations, the line measurements are found in excellent agreement with the theory. Previous studies in TMMC are discussed in light of these results.