  We study the formation of azimuthons, i.e., rotating spatial solitons, in
media with nonlocal focusing nonlinearity. We show that whole families of these
solutions can be found by considering internal modes of classical non-rotating
stationary solutions, namely vortex solitons. This offers an exhaustive method
to identify azimuthons in a given nonlocal medium. We demonstrate formation of
azimuthons of different vorticities and explain their properties by considering
the strongly nonlocal limit of accessible solitons.
