The correlation properties of some spreading sequences when applied to a system using nonlinear OQPSK-type signals is the main focus of this paper. These signals include, as special cases, CPM schemes (Continuous-Phase Modulation), which can be designed to have very low envelope fluctuations or even a constant envelope, making them compatible with a very low cost and power efficient grossly nonlinear amplification. We use an analytical method to derive both the autocorrelation and the cross-correlation of those signals. The resulting expressions are then applied to Gold Codes, Maximum-Length Sequences (MLS) and TCH (Tomlinson, Cercas, Hughes) sequences. It is shown that TCH sequences have better autocorrelation and cross-correlation properties than the other spreading sequences.