Nanopowders (NP) of yttrium-aluminium garnet (YAG) and/or yttrium aluminium perovskite (YAP) doped by rare-earth ions were studied as a prospective material for transparent scintillating ceramics. The YAG and YAP NP with the grain size ~20 nm and higher were obtained by coprecipitation method. Nominally pure, Ce3+, Nd3+ and Eu3+ doped NP have been studied by means of time-resolved luminescence spectroscopy. Pulsed electron beam (energy of electrons was 280 keV, pulse duration was 8 ns) was applied for luminescence excitation in 80-300 K temperature range. Intrinsic luminescence and energy transfer from the host lattice to rare-earth ions are competing relaxation channels. Time-resolved characteristics were measured for both intrinsic and dopand emissions. Results obtained may be summarized as follows: 1) Intrinsic luminescence bands were detected in all samples studied except cerium doped YAG NP. These bands are similar to well known emission for single- and poly- crystals. It means that centers (defects) responsible for unwanted intrinsic luminescence persist in NP. On the other hand no new (if compare with crystals) intrinsic luminescence bands appeared due to nanocrystalline structure. The reason of the absence of intrinsic luminescence in cerium doped NP will be discussed. 2) Luminescence decay kinetics of rare-earth ions strongly depends on dopand concentration and NP grain size. It is shown that the relaxation time for rare-earth related emission for NP is faster than for crystals with similar impurity concentration. 3) At low temperature after an excitation pulse a significant rise front of rare-earth related luminescence was observed. The rise front is strongly dependent on rare-earth ions concentration and temperature. The experimental facts allow us to suggest that energy transfer from the host lattice to the rare-earth ions differs in NP and crystals and an appropriate model will be suggested and discussed.