In 1-xGaxAs layers have been grown on InP(0 0 1) substrate for x = 0, 0. 18, 0.75, 1. The stress supported by epilayers then evolves from compression to tension. The morphology of the growth surface was studied by scanning tunnelling microscopy, first under arsenic surface overpressure, then under cation species surface overpressure. While the former situation leads to a 2D-3D growth mode transition in the case of compression and a surface roughening in the case tension, the initial flat 2D growth mode persists at even larger deposits in the latter situation. The whole of these results could be rationalised by considering the competition between stress relaxation and surface energy. It is shown that nanostructuring of the surface by way of a 2D-3D growth transition only takes place when step edges at 2D terraces can reach a critical height. This can be realised for high compression stress and low surface energy conditions, while a high surface energy favours a continued 2D growth at both compression or tension stresses. (C) 2004 Elsevier B.V. All rights reserved.