  Free massless fermionic fields of arbitrary spins $s>0$ corresponding to
totally (anti)symmetric tensor-spinor representations of the $SO(d-1)$ compact
subgroup and in $d$-dimensional anti-de Sitter space are investigated. We
propose the free equations of motion, subsidiary conditions and corresponding
gauge transformations for such fields. The equations obtained are used to
derive the lowest energy values for the above-mentioned representations. A new
representation for equations of motion and gauge transformations in terms of
generators of anti-de Sitter group $SO(d-1,2)$ is found. It is demonstrated
that in contrast to the symmetric case the gauge parameter of the antisymmetric
massless field is also a massless field.
