Sound transmission through a fluctuating deep ocean environment is considered. It is assumed that the environment consists of a range-independent background, on which a small-scale perturbation, due for example to internal waves, is superimposed. The modal description of underwater sound propagation is used extensively. The temporal spread of modal group arrivals in weakly range-dependent deep ocean environments is considered. The phrase "modal group arrival" refers to the contribution to a transient wavefield corresponding to a fixed mode number. It is shown that there are three contributions to modal group time spreads which combine approximately in quadrature. These are the reciprocal bandwidth, a deterministic dispersive contribution, and a scattering-induced contribution. The latter two contributions are shown to be proportional to the waveguide invariant beta, a property of the background sound speed profile. The results presented are based mostly on asymptotic theory. Some extensions of the asymptotic modal theory are developed. These theoretical results are shown to agree well with full-wave numerical wavefield simulations and available exact mode theoretical results. Theoretical predictions of modal group time spreads are compared to estimates derived from data that was collected during the 2004 LOAPEX experiment. The effects of deficiencies in the receiving array on estimates of modal group time spreads are discussed. It is shown that in spite of array deficiencies in the LOAPEX measurements it is possible to estimate modal group time spreads for almost all propagating modes and these estimates agree well with results obtained from numerical simulations and the developed theory. The effect of ocean internal waves on sound speed fluctuations is also considered, motivated by the observation that the amount of energy being scattered along the propagation path is sometimes greater in the experimental data than predicted by numerical simulations and theory. It is shown that the usual assumption that the potential sound speed gradient is proportional to the squared buoyancy frequency is often not a good approximation.