||Spread Spectrum (SS) is a powerful technique to improve the robustness and reliability of communications in the presence of severe noise and interferences. Owing to the difficulty in achieving perfect synchronism of the transmitted signals at the receiver, SS systems designed to accommodate quasi-synchronism and asynchronism have a much wider range of real-world applications than synchronous SS systems. For Quasi-Synchronous Spread Spectrum (QS-SS) communications, good design of spreading sequences should have an impulse-like autocorrelation function even under the effect of quasi-synchronism, M-ary phase-shift-keying (M-PSK) data modulation as well as multipath inter-symbol interference (lSI). In this work, the criterion of dual-window low correlation zone is proposed. Best dual window sequences are searched and tabulated. Extension of the results to multiuser QS-SS (or QS-CDMA) systems with insignificant lSI can be achieved by deriving an orthogonal set of dual-window sequences by applying the so-called generalized Oppermann transform to any individual sequence obtained by our search. The mutual orthogonality property of these sequences ensures zero in-phase multiple access interference while their dual-window property enhances the resistance to receiver synchronization error. The size of two types of such orthogonal sequence sets have been analyzed and they depend on the parity of the sequence length involved. In an Asynchronous Spread Spectrum (A-SS) system, as relative delays between signals transmitted can be arbitrary, it is desirable to find spreading sequences with low aperiodic autocorrelation functions. The associated sequence search problem is classical and is well-known to be NP-hard. Therefore, searching for long spreading sequences for A-SS is very challenging and exhaustive search is not a feasible method. In this work, we propose a novel nonlinear optimization approach with the incorporation of evolutionary algorithms. The search results show that the proposed methodology can discover new binary sequences for lengths up to 4096 with their peak sidelobe levels better than those reported in the recent literature.