  We verify the existence of Generalized Sudden Future Singularities (GSFS) in
quintessence models with scalar field potential of the form $V(\phi)\sim \vert
\phi\vert^n$ where $0<n<1$ and in the presence of a perfect fluid, both
numerically and analytically, using a proper generalized expansion ansatz for
the scale factor and the scalar field close to the singularity. This
generalized ansatz includes linear and quadratic terms, which dominate close to
the singularity and cannot be ignored when estimating the Hubble parameter and
the scalar field energy density; as a result, they are important for analysing
the observational signatures of such singularities. We derive analytical
expressions for the power (strength) of the singularity in terms of the power
$n$ of the scalar field potential. We then extend the analysis to the case of
scalar tensor quintessence models with the same scalar field potential in the
presence of a perfect fluid, and show that a Sudden Future Singularity (SFS)
occurs in this case. We derive both analytically and numerically the strength
of the singularity in terms of the power $n$ of the scalar field potential.
