  Here we define the concept of Qregularity for coherent sheaves on quadrics.
In this setting we prove analogs of some classical properties. We compare the
Qregularity of coherent sheaves on $\Q_n\subset \mathbb P^{n+1}$ with the
Castelnuovo-Mumford regularity of their extension by zero in $\mathbb P^{n+1}$.
We also classify the coherent sheaves with Qregularity $-\infty$. We use our
notion of Qregularity in order to prove an extension of Evans-Griffiths
criterion to vector bundles on Quadrics. In particular we get a new and simple
proof of the Kn\"{o}rrer's characterization of ACM bundles.
