Variable coherence microscopy shows that as-deposited amorphous germanium and silicon contain medium-range order. The ordering can be explained by a fine-grained paracrystallite material in which intergranular stress has been relaxed by deformation. On annealing, the paracrystallite structure transforms towards the lower-energy continuous random network (CRN). We present data on a variety of vacuum-evaporated samples, and on molecular dynamics simulations of candidate structures. (C) 1998 Elsevier Science B.V. All rights reserved.