  The definition of ``Lie derivative'' of spinors with respect to Killing
vectors is extended to all kinds of Lorentz tensors. This Lie-Lorentz
derivative appears naturally in the commutator of two supersymmetry
transformations generated by Killing spinors and vanishes for Vielbeins. It can
be identified as the generator of the action of isometries on supergravity
fields and its use for the calculation of supersymmetry algebras is revised and
extended.
