  The present work is an extensive study of the viable stable solutions of
chameleon scalar field models leading to possibilities of an accelerated
expansion of the universe. It is found that for various combinations of the
chameleon field potential $V(\phi)$ and the coupling $f(\phi)$ of the chameleon
field with matter, a stable solution for an accelerated expansion is quite
possible. The investigation provides a diagnostics for the stability criteria
for all sorts of combinations of $V(\phi)$ and $f(\phi)$.
