The quantized vortex in a superfluid or superconducting Fermi system may contain gapless fermionic excitations localized in the vortex core. The number of branches of the gapless excitations-fermionic zero modes-depends on the core structure and may change from 0 to epsilon _F/ Delta >>1. The author investigated the possibility of the existence of the fermionic zero modes localized in the cores of axisymmetric vs. vortices in superfluid ³He-B. The zero modes exist if the core radius exceeds the coherence length.