  The classification problem for conformally-flat space-times that admit a
separation of variables in the Hamilton-Jacobi equation of the scalar-tensor
Brans-Dicke theory of gravity is examined. The field equations of the
scalar-tensor theory of Brans and Dicke for conformally-flat Stackel
space-times of type (1.1) are solved. An explicit form of the metric tensor and
scalar field is obtained.
