Collisional particle transport is examined in several toroidal plasma devices in the presence of perturbations typical of modes leading up to a disruption, of saturated tearing modes, or of unstable Alfvén modes. The existence of subdiffusive transport for electrons is found to occur in some cases at very low mode amplitudes and to also exist even for ions of high energy. Orbit resonances can produce long time correlations and traps for particle trajectories at perturbation amplitudes much too small for the orbits to be represented as uniformly chaotic. The existence and nature of subdiffusive transport is found to depend on the nature of the mode spectrum and frequency as well as the mode amplitudes.