  We present a space-time generalization of the known spatial (monochromatic)
wave vortex beams carrying intrinsic orbital angular momentum (OAM) along the
propagation direction. Generic spatio-temporal vortex beams are polychromatic
and can carry intrinsic OAM at an arbitrary angle to the mean momentum.
Applying either (i) a transverse wave-vector shift or (ii) a Lorentz boost to a
monochromatic Bessel beam, we construct a family of either (i) time-diffracting
or (ii) non-diffracting spatio-temporal Bessel beams, which are exact solutions
of the Klein-Gordon wave equations. The proposed spatio-temporal OAM states are
able to describe either photon or electron vortex states (both relativistic and
nonrelativistic), and can find applications in particle collisions, optics of
moving media, quantum communications, and astrophysics.
