Stray electrons can be introduced in heavy ion fusion accelerators as a result of ionization of ambient gas or gas released from walls due to halo-ion impact, or as a result of secondary- electron emission. We summarize here results from several studies of electron-cloud accumulation and effects: (1) Calculation of the electron cloud produced by electron desorption from computed beamion loss; the importance of ion scattering is shown; (2) Simulation of the eect of specified electron cloud distributions on ion beam dynamics. We find electron cloud variations that are resonant with the breathing mode of the beam have the biggest impact on the beam (larger than other resonant and random variations), and that the ion beam is surprisingly robust, with an electron density several percent of the beam density required to produce significant beam degradation in a 200-quadrupole system. We identify a possible instability associated with desorption and resonance with the breathing mode. (3) Preliminary investigations of a long-timestep algorithm for electron dynamics in arbitrary magnetic fields.