  In this work a proposal for definition of twistors on generic curved spaces
is exposed and investigated. We consider superpositions of nearly autoparallel
and nearly geodesic maps (nearly conformal maps, nc-maps) of
(pseudo-)Riemannian spaces as generalizations of conformal transforms. We
introduce the nearly autoparallel twistor equations being compatible on nc-flat
spaces and study nearly autoparallel twistor structures generating curved
spaces and vacuum Einstein equations.
