Stars showing very small amplitudes of radial velocity have been inter
preted as systems having planetary companions. For some of them, we pr
esent an alternative interpretation in which the star would be a binar
y system seen face-on, a scheme relying mainly on the fact that the ob
served amplitude of radial velocity is determined from the blended lin
es of two stars having close parameters. This model very satisfactoril
y explains the observational data of 47 UMa, 70 Vir and 16 Cyg B with,
however, a low probability. Such systems will certainly occur in the
case of large samples. We conclude that in the limited samples availab
le for the moment, almost all the systems with very small amplitudes o
f radial velocity variations must be considered as planetary systems.