We study the asymptotic behaviour, as the retarded time
u tends to infinity, of the solutions of Einstein's equations in the spherically symmetric case with a massless scalar field as the material model. We prove that when the final Bondi mass
M
1 is different from zero, as
u 
, a black hole forms of mass
M
1 surrounded by vacuum. We find the rate of decay of the metric functions and the behaviour of the scalar field on the horizon.
Communicated by S.-T. Yau
Research supported in part by National Science Foundation grants MCS-8201599 to the Courant Institute and PHY-8318350 to Syracuse University