Molecular magnets Cu(hfac)(2)L-R represent a new type of photoswitchable materials based on exchange-coupled clusters of copper(II) with stable nitroxide radicals. It was found recently that the photoinduced spin state of these compounds is metastable on the time scale of hours at cryogenic temperatures, similar to the light-induced excited spin state trapping phenomenon well-known for many spin-crossover compounds. Our previous studies have shown that electron paramagnetic resonance (EPR) in continuous wave (CW) mode allows for studying the light-induced spin state conversion and relaxation in the Cu(hfac)(2)L-R family. However, light-induced spin dynamics in these compounds has not been studied on the sub-second time scale so far. In this work we report the first time-resolved (TR) EPR study of light-induced spin state switching and relaxation in Cu(hfac)(2)L-R with nanosecond temporal resolution. To enhance spectral resolution we used high-frequency TR EPR at W-band (94 GHz). We first discuss the peculiarities of applying TR EPR to the solid-phase compounds Cu(hfac)(2)L-R at low (liquid helium) temperatures and approaches developed for photoswitching/relaxation studies. Then we analyze the kinetics of the excited spin state at T = 5-21 K. It has been found that the photoinduced spin state is formed at time delays shorter than 100 ns. It has also been found that the observed relaxation of the excited state is exponential on the nanosecond time scale, with the decay rate depending linearly on temperature. We propose and discuss possible mechanisms of these processes and correlate them with previously obtained CW EPR data.