We study string propagation in an anisotropic, cosmological background. We
solve the equations of motion and the constraints by performing a perturbat
ive expansion of the string coordinates in powers of c(2) - the worldsheet
speed of light. To zeroth order the string is approximated by a tensionless
string (since c is proportional to the string tension T). We obtain exact,
analytical expressions for the zeroth- and first-order solutions and pie d
iscuss some cosmological implications.