A theory is presented for the radiation at the third to fifth harmonics of the plasma frequency observed upstream from the Earth's bow shock: the radiation is produced by the process L+T'→T in the foreshock, with the initial T' radiation being the frequently observed second harmonic radiation (generated by another process) and the L waves being products of the decay L'→L+S of L' waves generated by a streaming instability. (Here L, S, and T denote Langmuir, ion acoustic, and 'transverse electromagnetic waves, respectively.) The theory can account for the observed radiation when unusually large levels (electric fields in excess of 10 mV/m) of suitable L waves are present. Such levels of L waves are possible, in principle, but have not been reported before; the radiation is observed quite infrequently, thereby implying a requirement for unusual foreshock conditions. Predictions for the characteristics of the source regions (one to each wing of the foreshock) and the bandwidth of the radiation are given. Potential problems for the theory, relating to the large levels of L waves required to account for the radiation, are discussed. ¿ American Geophysical Union 1988