This paper deals with the new family of partial-response-signalling-continuous-phase-modulation (PRS-CPM) which is the triple-chirp-modulation (TChM). The elementary frequency pulses and the modulated signal general description are given, together with an example of a phase tree. Due to the shape of an elementary frequency pulse, modulated signal phase trajectories are bounded, and the finite state machines of modulators and Viterbi detectors are independent of the modulation index h. An example of a TChM finite state diagram is presented for L=4. Investigations of the TChM error performance on AWGN channel and spectral analysis, with comparisons to MSK, are carried out. It is shown that the error performance of TChM on an AWGN channel is for selected values of the shape parameters better than the error performance of MSK. For that reason, the application of TChM in future mobile radio systems could be possible.