  We study the interplay between basic Dirac operator and transverse Killing
and twistor spinors. In order to obtain results for general Riemannian
foliations with bundle-like metric we consider transverse Killing spinors that
appear as natural extension of the harmonic spinors associated with the basic
Dirac operator. In the case of foliations with basic-harmonic mean curvature it
turns out that these Killing spinors and twistor spinors coincide with the
standard definition. We obtain the corresponding version of classical results
on closed Riemannian manifold with spin structure, extending some previous
results.
