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We propose a new spread spectrum (SS) system based on continuous-phase modulations (CPMs). The main idea is to exploit the sequence of modulation indices of a multi-h CPM as a frequency-hopping (FH) sequence. Spectral spreading, flatness and smoothness can be easily achieved by an appropriate choice of the maximum value of the modulation index and of the length of the index sequence. We will show that the proposed CPM-based spread spectrum system achieves an overall spectral efficiency larger than that of a single-user single-h CPM transmission even when a single-user detector is employed at the receiver. It also outperforms other solutions in the literature. In addition, we will also derive some suboptimal multi-user detectors.