  The paper consists of three parts. In the first of them different kinds
stability are discussed. In particular, the stability concept with respect to
nef divisor is introduced. A structure of rigid and superrigid vector bundles
on smooth projective surfaces with nef anticanonical class is studied in the
second part. We prove that any superrigid bundle has a unique exceptional
filtration. In the last part we give constructive description of exceptional
bundles on these surfaces.
