  We introduce and study a new class of differential fields in positive
characteristic. We call them separably differentially closed fields and
demonstrate that they are the differential analogue of separably closed fields.
We prove several (algebraic and model-theoretic) properties of this class.
Among other things, we show that it is an elementary class, whose theory we
denote $\SDCF$, and that its completions are determined by specifying the
characteristic $p$ and the differential degree of imperfection $\epsilon$.
Furthermore, after adding what we call the differential $\lambda$-functions, we
prove that the theory $\SDCFl$ admits quantifier elimination, is stable, and
prime model extensions exist.
