  In this paper we describe six pencils of K3-surfaces which have large
Picard-Number and contain precisely five singular fibers: four have A-D-E
singularities and one is non-reduced. In particular we describe these surfaces
as cyclic coverings of the K3-surfaces which Barth and the author described in
a previous manuscript (Asian. J. of Math. Vol. 7, No. 4, 519-538, Dec. 2003).
In many cases using this description and lattice-Theory we are able to compute
the exact Picard-number and to describe explicitly the Picard-lattices.
