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Binary continuous phase modulations with constant amplitude (CPM) with modulation index 1/2 have been shown to provide both good spectral and error probability properties. These modulations can also be detected with a very simple linear detector, which can be implemented simply at high speeds. This can be done with only a minor degradation in error performance. The linear detector can be implemented both as a serial and as a parallel detector, and these have slightly different sensitivity to errors in bit timing and phase synchronisation. In the paper we study the effects of multiple interfering signals on both these linear detectors for CPM. Coherent detection is assumed, and both Gaussian and slow Rayleigh fading channels are considered. Analytical formulas are derived on both channels, where only a single integral has to be calculated numerically. This formula can also easily be used for detector filters with impulse response of long time duration. It is shown that the difference in performance due to the number of interferers is small, when the total interference power is kept constant. Further, it is shown that the performance is improved by several decibels for the longer asymptotically optimum filters in adjacent channel interference. As one would expect, the smoothed phase modulations have significantly larger tolerances against adjacent channel interference, while the difference is small in cochannel interference. On the Rayleigh fading channel, the longer asymptotically optimum filters on the Gaussian channel lead to much lower irreducible error probabilities than does the MSK filter; a decrease by a factor of as much as 10 has been found.