  We present and analyze new exact gyraton solutions of algebraic type II on a
background which is static, cylindrically symmetric Melvin universe of type D.
For a vanishing electromagnetic field it reduces to previously studied gyratons
on Minkowski background. We demonstrate that the solutions are member of a more
general family of the Kundt spacetimes. We show that the Einstein equations
reduce to a set of mostly linear equations on a transverse 2-space and we
discuss the properties of polynomial scalar curvature invariants which are
generally non-constant but unaffected by the presence of gyratons.
