  The Neron--Ogg--Safarevic criterion for abelian varieties tells that whether
an abelian variety has good reduction or not can be determined from the Galois
action on its l-adic etale cohomology. We prove an analogue of this criterion
for some special kind of K3 surfaces (those which admit Shioda--Inose
structures of product type), which are deeply related to abelian surfaces. We
also prove a p-adic analogue. This paper includes Ito's unpublished result for
Kummer surfaces.
