  We are interested in the multi-dimentional compressible viscoelastic flows of
Oldroyd type, which is one of non-Newtonian fluids exhibiting the elastic
behavior. In order to capture the damping effect of the additional deformation
tensor, to the best of our knowledge, the "div-curl" structural condition plays
a key role in previous efforts. Our aim of this paper is to remove the
structural condition and prove a global existence of strong solutions to
compressible viscoelastic flows in critical spaces. The new ingredient lies in
the introduction of effective flux $(\theta,\mathcal{G})$, which enables us to
capture the dissipation arising from \textit{combination} of density and
deformation tensor. In absence of compatible conditions, the partial
dissipation is found in non-Newtonian compressible fluids, which is weaker than
that of usual Navier-Stokes equations.
