  We provide a proof of global regularity of solutions of some models of
viscoelastic flow with an integral constitutive law, in the two spatial
dimensions and in a periodic domain. Models that are included in these results
are classical models for flow memory: for instance some K-BKZ models, the PSM
model or the Wagner model. The proof is based on the fact that these models
naturally give a $L^\infty$-bound on the stress and that they allow to control
the spatial gradient of the stress. The main result does not cover the case of
the Oldroyd-B model.
