Sinusoidally modulated ZnSeTe superlattices were fabricated by means of a novel MBE growth technique, in which the periodic modulation is achieved by substrate rotation in the presence of non-uniform flux distributions of Se and Te, rather than by shutter openings and closings. The sinusoidal modulation of composition in the system naturally leads to a sinusoidal energy band profile, which in turn is expected to result in new and unique optical and electronic properties. We have performed extensive photoluminescence (PL) measurements on a series of sinusoidal ZnSeTe superlattices having various degrees of compositional modulation (i.e., various band offsets) and various periods. The observed transition energies in these superlattices can be successfully analyzed in terms of an adaptation of the nearly free electron model.