Rapidly oscillating Ap (roAp) stars are cool magnetic Ap SrCrEu stars which pulsate in high-overtone (n ≫ l), low-degree (ℓ ≤ 3) p-modes, with periods from 6 to 15 minutes and typical amplitudes of a few millimagnitudes. 28 such stars are currently known. The roAp phenomenon is confined to a well-defined region of the Strömgren photometry parameter space. However, this region also contains other Ap stars, in which no pulsation could be detected, despite sometimes thorough searches. These apparently constant Ap stars (non-oscillating Ap stars, or noAp stars) appear remarkably similar to the roAp stars in many respects (e.g. colour indices, abundances, magnetic fields). Here we present recently found indications for differences between both groups.