Oscillitons are stationary, nonlinear structures exhibiting spatial oscillations superimposed on the spatial growth and decay which is characteristic of usual solitons. Although they were first identified in plasmas with two ion populations, it is shown they may generally occur in any media with a particular wave dispersion, in which there is at least one point in the diagnostic diagram where the phase- and group velocities coincide at finite values of k. In this paper, we study the properties of oscillitons in the electron whistler branch ('whistler oscillitons'). These arise from the momentum exchange between protons and electrons, mediated by the Maxwell stresses, and may generate coherent wave packets in the frequency range of 0.1 Ωe ≤ ω ≤ 0.5 Ωe (Ωe: electron cyclotron frequency), depending on ¿e (¿e = 2¿onkTe/B2) and the temperature anisotropy T⊥e/T∥e. Applications to observations of 'coherent lion roars' are discussed.