  We study the structure of a modified Fukaya category ${\frak F}(X)$
associated with a K3 surface $X$, and prove that whenever $X$ is an elliptic K3
surface with a section, the derived category of $\fF(X)$ is equivalent to a
subcategory of the derived category ${\bold D}(\hat X)$ of coherent sheaves on
the mirror K3 surface $\hat X$.
