The transport times τ(P) and the mean free paths of magnetoexcitons in a quantum well and of spatially direct and indirect magnetoexcitons in coupled quantum wells in a random potential produced by thickness fluctuations of the quantum wells or a random distribution of impurity centers in quantum wells (P is the magnetic momentum of an exciton) are calculated. The function τ(P) is nonmonotonic, but as the distance D between the quantum wells increases, the maximum τ max(P) gradually vanishes in the presence of scattering by surface terraces. As the magnetic field (H) increases, τ(0) decreases as $${1 \mathord{\left/ {\vphantom {1 {\sqrt H }}} \right. \kern-\nulldelimiterspace} {\sqrt H }}$$ for $$D \ll l(l = {{\sqrt {\hbar c} } \mathord{\left/ {\vphantom {{\sqrt {\hbar c} } {eH}}} \right. \kern-\nulldelimiterspace} {eH}}$$ is the magnetic length) and as 1/H 2 for D≫l. The behavior of the computed values of τ for large H agrees qualitatively with the experimental data. The mean free path length of a magnetoexciton exhibits at P≠0 a maximum whose magnitude decreases as the parameter D/l increases.