  We consider the correspondence between the Jordan frame and the Einstein
frame descriptions of scalar-tensor theory of gravitation. We argue that since
the redefinition of the scalar field is not differentiable at the limit of
general relativity the correspondence between the two frames is lost at this
limit. To clarify the situation we analyse the dynamics of the scalar field in
different frames for two distinct scalar-tensor cosmologies with specific
coupling functions and demonstrate that the corresponding scalar field phase
portraits are not equivalent for regions containing the general relativity
limit. Therefore the answer to the question whether general relativity is an
attractor for the theory depends on the choice of the frame.
