  We study solutions describing spinning null sources called gyratons in
generic theories of gravity with terms that are quadratic in curvature and
contain an arbitrary number of covariant derivatives. In particular, we show
that the properties of pp-waves of the algebraic type III allow for extreme
simplification of the field equations. It turns out that the resulting
differential equations are exactly solvable due to partial decoupling and
linearity of the equations. This is demonstrated explicitly by finding axially
symmetric gyraton solutions in Stelle's fourth derivative gravity and the
non-local gravity with an infinite number of derivatives.
