The adsorption and desorption of Se on the Si(0 0 1) surface are investigated, based upon the ab initio pseudopotential calculations. Following a recent experimental work, three different adsorption models have been studied: 1/2 NIL of Se on the Si-Si dimer with a bridge position within the (1 x 2) surface reconstruction, 1 ML of Se sitting above the topmost Si atoms in bridge absorption site within the (1 x 1) surface reconstruction, and 2 M L of Se half of which is embedded into the Si bulk near the surface within the (1 x 1) surface reconstruct ion. For 1/2 ML, we have found that the vertical displacement between the Se atom and Si-Si dimer is 1.97 Angstrom, close to the experimentally measured value of 2.10 Angstrom. For I ML, the vertical displacement between the Se atom and the Si atoms is 1.41 Angstrom, somewhat smaller than the experimentally measured value of 1.60 Angstrom, For 2 ML, upon relaxation, the embedded Se atoms have diffused upwards. Our results are analysed to provide support to a recent experimental study of desorption of Se from the surface. (C) 2002 Elsevier Science B.V. All rights reserved.