This paper investigates the main correlation properties of some spreading sequences when applied to a system using nonlinear OQPSK-type modulations, since this is an important topic for present and future wireless communications. These signals, that include as special cases CPM schemes (Continuous-Phase Modulation), 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 Maximum-Length (ML) sequences, Gold Codes and TCH (Tomlinson, Cercas, Hughes) sequences. It is shown that TCH sequences have better autocorrelation and cross-correlation properties when submitted to a nonlinear system. These results can be applied in multi-user detection, spreading, synchronization, channel estimation and many other relevant issues for the radio interface of any communication system.