The addition of small amounts of niobium or tantalum oxide to lithium disilicate glass provokes a drastic decrease of the steady-state nucleation rates and the crystal growth velocities. The viscosity of the residual glassy matrix is considered as a function of the crystallization degree in the course of a non-isothermal crystallization. For simplification, a homogeneous distribution of the added oxides in the glass matrix is assumed. While the viscosity initially decreases, it significantly increases again for higher crystallization degrees hindering crystal growth. However, it was shown that the additives are enriched at the crystal interface. Several possible reasons for the inhibition of nucleation and growth kinetics such as viscosity, interfacial energy crystal/glassy phase, thermodynamic driving force or impingement rate are discussed. Since the crystallization front is blocked by the additives the impingement rate is decreased with increasing additive concentration. Since small concentrations of Nb2O5 and Ta2O5 have a drastic effect on the nucleation, these components should be enriched at the interface crystal/glass. This will only take place, if it leads to a decrease in the interfacial energy. Since this effect alone should result in an increase of the nucleation rate, it must be overcompensated by kinetic effects.