  The enhanced star forming activity, typical of starburst galaxies, powers
strong galactic winds expanding on kpc scales and characterized by bubble
structures. Here we discuss the possibility that particle acceleration may take
place at the termination shock of such winds. We calculate the spectrum of such
particles and their maximum energy, that turns out to be in the range $\sim
10-10^2$ PeV for typical values of the parameters. Cosmic rays accelerated at
the termination shock can be advected towards the edge of the wind bubble and
eventually escape into extragalactic space. We also calculate the flux of gamma
rays and neutrinos produced by hadronic interactions in the bubble as well as
the diffuse flux resulting from the superposition of the contribution of
starburst galaxies on cosmological scales. Finally we compute the diffuse flux
of cosmic rays from starburst bubbles and compare it with existing data.
