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Single-carrier frequency-domain equalization (SC-FDE) is proposed for continuous phase modulation (CPM). Two different discrete representations of the CPM signal are obtained. One is an orthogonal representation obtained from the Gram-Schmidt orthonormalization procedure, and the other is obtained from Laurent's decomposition for binary CPM. The methodology for maintaining phase continuity with a cyclic guard interval is presented. Various optimal and suboptimal reduced-complexity approaches are suggested for SC-FDE of CPM signals. General full- and partial-response CPM waveforms, and specific examples of minimum-shift keying (MSK) and Gaussian MSK (GMSK) with BT=0.3 are investigated. Simulation results show that SC-FDE for CPM is an effective approach for CPM on channels having long impulse responses.