In the astronomical literature, spin-orbit coupling is described in two approaches, both of which were pioneered in the seminal paper by Goldreich and Peale (1966). The "MacDonald torque", based on a tidal theory of Gerstenkorn (1955) and MacDonald (1964), has long become the textbook standard (Kaula 1968, Murray and Dermott 1999) due to its apparent simplicity. The "Darwin torque" rests on a more fundamental theory by Darwin (1879, 1880) and Kaula (1964). While their theory is general enough to accommodate an arbitrary frequency-dependence of Q, this advantage has not yet been exploited in the literature, where Q is either assumed constant or set to scale as inverse tidal frequency, the latter assertion making the Darwin torque equivalent to a corrected version of the MacDonald torque. However neither a constant Q nor an inverse-frequency Q reflect the properties of realistic mantles and crusts, because the actual frequency-dependence of the quality factor is complex. Hence the necessity to enrich the Darwin-Kaula theory with the right frequency-dependence. Both the MacDonald- and Darwin-torque-based theories of despinning were reconsidered by Efroimsky and Williams (2008), in application to spin modes distant from commensurabilities. In the current paper, we continue this work by introducing the necessary alterations into the MacDonald- and Darwin-torque-based models near resonances. We derive the frequency-dependence of the tidal torque from the first principles, i.e., from the expression for the mantle's compliance in the time domain. We also explain that the tidal torque includes not only the customary, secular part, but also an oscillating part. Normally, only the constant part of the torque is taken into account in despinning problems. We point out that the oscillating part, too, has to be taken into consideration, when entrapment into a resonance is considered.