Pseudo-Noise (PN) sequences are widely used in, from simple applications such as clock dividers to complex applications such as spread spectrum communication systems. Among PN sequences, maximal length (m-)sequences are very popular for communications and ranging applications, due to their desirable properties. While m-sequences are available only in limited number of lengths, the non-maximal length (NML) sequences are available in varieties of lengths. It appears that the NMLS were not investigated into, to the extent they deserve. The author conjectures that several other (noncommunications) applications might benefit from the NLM sequences. In this paper, generation and periodicity property of NLM sequences, corresponding to polynomials of degree 3 to 20 are investigated. The results are expected to create an interest among the researchers in exploring some new applications of NML sequences.