  We study antigravity, that is having an effective gravitational constant with
a negative sign, in scalar-tensor theories originating from $F(R)$-theory and
in a Brans-Dicke model with cosmological constant. For the $F(R)$ theory case,
we obtain the antigravity scalar-tensor theory in the Jordan frame by using a
variant of the Lagrange multipliers method and we numerically study the time
dependent effective gravitational constant. As we shall demonstrate by using a
specific $F(R)$ model, although there is no antigravity in the initial model,
it might occur or not in the scalar-tensor counterpart, mainly depending on the
parameter that characterizes antigravity. Similar results hold true in the
Brans-Dicke model.
