Exact plane wave solutions of d = 10, N = 1 Einstein-Yang-Mills supergravity theory are presented and their possible modifications in superstring effective theories are examined. It is found that the solutions are not affected by any of the known heterotic string corrections. It is argued that plane waves satisfy the effective field equations of the heterotic string theory in all powers of the string tension parameter α', possibly after including a totally antisymmetric torsion field and reinterpreting the constants. Similar remarks also apply for type I superstrings. Further properties of the solutions are discussed.