  The behavior of nonperturbative parts of the isovector-vector and isovector
and isosinglet axial-vector correlators at Euclidean momenta is studied in the
framework of a covariant chiral quark model with nonlocal quark-quark
interactions. The gauge covariance is ensured with the help of the P-exponents,
with the corresponding modification of the quark-current interaction vertices
taken into account. The low- and high-momentum behavior of the correlators is
compared with the chiral perturbation theory and with the QCD operator product
expansion, respectively. The V-A combination of the correlators obtained in the
model reproduces quantitatively the ALEPH data on hadronic \tau decays,
transformed into the Euclidean domain via dispersion relations. The predictions
for the electromagnetic \pi^\pm - \pi^0 mass difference and for the pion
electric polarizability are also in agreement with the experimental values. The
topological susceptibility of the vacuum is evaluated as a function of the
momentum, and its first moment is predicted to be \chi'(0)\approx (50 MeV)^2.
In addition, the fulfillment of the Crewther theorem is demonstrated.
