A theory of the nucleation of crystalline particles in disordered medi
a is proposed accounting for small statistical fluctuations in microsc
opic structural parameters, which are shown to affect considerably the
thermodynamic barrier to nucleation. As a result, the classical nucle
ation-rate exponent -W/kT takes the correction GAMMA (W/kT)3 at high t
emperatures, where GAMMA depends both on the correlation radius of the
disorder and its amplitude; this correction may be significant. At lo
w temperatures the nucleation-rate exponent remains finite in the case
of uncorrelated disorder, while it is proportional to T-1/3 at T -->
0 in the case of strongly correlated disorder. The implications of the
se findings for nucleation in glasses are discussed.