A generic ansatz is introduced which provides families of exact solutions to
the equations of motion and constraints for null-strings in Bianchi type I
cosmological models. This is achieved irrespective of the form of the metric.
Within classes of dilaton cosmologies a backreaction mapping relation is
established where the null string leads to more or less anisotropic members of
the family. The equations of motion and constraints for the generic model are
casted in their first order form and integrated both analytically and
numerically.Comment: 37 pages, 11 figure