We study asymptotic behavior in a class of non-autonomous second order parabolic equations with time periodic unbounded coefficients in $mathbb Rtimes mathbb R^d$. Our results generalize and improve asymptotic behavior results for Markov semigroups h
aving an invariant measure. We also study spectral properties of the realization of the parabolic operator $umapsto {cal A}(t) u - u_t$ in suitable $L^p$ spaces.
