  We survey motivation, basic ideas and physical consequences of a theory where
the underlying action involves terms both with the usual volume element
$\sqrt{-g}d^{4}x$ and with the new one $\Phi d^{4}x={4!}d\varphi_{1}\wedge
d\varphi_{2}\wedge d\varphi_{3}\wedge d\varphi_{4}$. The latter may be
interpreted as the 4-form determined on the 4-D space-time manifold (not
necessary Riemannian). Regarding the scalar fields $\varphi_{a} (a=1,...4)$ as
new dynamical variables and proceeding in the first order formalism we realize
the so-called Two Measures Theory which possesses a number of attractive
features. We discuss new physical effects which arise from this theory and in
particular strong gravity effect in high energy physics experiments.
