  We compute the 2- and 3-point functions of currents and primary fields of
$\lambda$-deformed integrable $\sigma$-models characterized also by an integer
$k$. Our results apply for any semisimple group $G$, for all values of the
deformation parameter $\lambda$ and up to order $1/k$. We deduce the OPEs and
equal-time commutators of all currents and primaries. We derive the currents'
Poisson brackets which assume Rajeev's deformation of the canonical structure
of the isotropic PCM, the underlying structure of the integrable
$\lambda$-deformed $\sigma$-models. We also present analogous results in two
limiting cases of special interest, namely for the non-Abelian T-dual of the
PCM and for the pseudodual model.
