  The stability of the cosmological event horizons (CEHs) of a class of
non-static global cosmic strings is studied against perturbations of
gravitational waves and massless scalar field. It is found that the
perturbations of gravitational waves always turn the CEHs into non-scalar weak
spacetime curvature singularities, while the ones of massless scalar field turn
the CEHs either into non-scalar weak singularities or into scalar ones
depending on the particular cases considered. The perturbations of test
massless scalar field is also studied, and it is found that they do not always
give the correct prediction.
