A theoretical model is developed according to which crystals formed in a glass-forming melt can exhibit a previously unreported growth behavior. After growing very fast in one or two directions, the growth stops due to changes in concentration and turns into dissolution. Along the other direction(s) the growth rate is initially lower; it also slows down but never becomes negative. This is the result of a competition between several processes that take place simultaneously in a nonequilibrium system. Due to direction-dependent growth rates (the latter can vary over a large range), such behavior may result in the first step in the formation of plate or needlelike crystals. After a drop in the concentration of some key compounds (the crystals are consuming the latter), in the second stage the crystals approach their equilibrium shape since relaxation processes prevail. It is demonstrated with an example (mica plates formed from an extruded glass) that such effects in fact can be found experimentally. Although at this initial stage the model is quite simplified it leads to a surprisingly good agreement with the experimental data. It seems that there are many other examples of processes in nonequilibrium systems in which a given parameter is developing, at early stages, far beyond its equilibrium value, and later (when the resources of the system are becoming exhausted and consequently the growth rates slow down) relaxation kinetics dominates.