High spectral resolution bidimensional spectroscopy of A78 in the He II λ4686 A, H λ4861 A, [O III] λ4959 A and [O III] λ5007 A lines is reported, confirming the different morphology of the nebula in these lines. The resulting velocity maps suggest different episodes in the history of the nebula, with an external hydrogen-rich layer expanding at low velocity (35±10 km/s), showing little structure and extending from approximately 35 to 55 arcsec. The [O III] and the He II maps show, however, an inner shell with at least two different expansion velocities; 73 km/s and 41 km/s.