Modern nanophotonics has witnessed the rise of “electric anapoles” (EDAs), destructive interferences of electric and toroidal electric dipoles, actively exploited to resonantly decrease radiation from nanoresonators. However, the inherent duality in Maxwell equations suggests the intriguing possibility of “magnetic anapoles,” involving a nonradiating composition of a magnetic dipole and a magnetic toroidal dipole. Here, a hybrid anapole (HA) of mixed electric and magnetic character is predicted and observed experimentally via dark field spectroscopy, with all the dominant multipoles being suppressed by the toroidal terms in a nanocylinder. Breaking the spherical symmetry allows to overlap up to four anapoles stemming from different multipoles with just two tuning parameters. This effect is due to a symmetry‐allowed connection between the resonator multipolar response and its eigenstates. The authors delve into the physics of such current configurations in the stationary and transient regimes and explore new ultrafast phenomena arising at sub‐picosecond timescales, associated with the HA dynamics. The theoretical results allow the design of non‐Huygens metasurfaces featuring a dual functionality: perfect transparency in the stationary regime and controllable ultrashort pulse beatings in the transient. Besides offering significant advantages with respect to EDAs, HAs can play an essential role in developing the emerging field of ultrafast resonant phenomena.