  In this note we study Morita contexts and Galois extensions for corings. For
a coring $\QTR{cal}{C}$ over a (not necessarily commutative) ground ring $A$ we
give equivalent conditions for $\QTR{cal}{M}^{\QTR{cal}{C}}$ to satisfy the
weak. resp. the strong structure theorem. We also characterize the so called
\QTR{em}{cleft}$C$\QTR{em}{-Galois extensions} over commutative rings. Our
approach is similar to that of Y. Doi and A. Masuoka in their work on (cleft)
$H$-Galois extensions.
