The linear theory of electromagnetic instabilities at propagation parallel or antiparallel to a uniform magnetic fieldB(0)is used to calculate the relative phase angle &psgr;jbetween the fluctuating velocity vector of the  jth component and the fluctuating magnetic field. A criterion that determines when this phase relationship leads to observable gyrophase bunching during the linear growth phase of an instability is also derived. The theory is applied to bunching of ion components by ion beam instabilities. Among the electromagnetic cool ion beam instabilities, it is found that the right‐hand resonant mode is most likely to cause observable gyrophase bunching of an ion beam during linear growth, and that for sufficiently large beam–core relative drift speeds, &psgr;b&bartil;90° at maximum growth for instability propagation parallel toB(0).