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In a cylinder $\Omega_T=\Omega\times (0,T)\subset \R^{n+1}_+$ we study theboundary behavior of nonnegative solutions of second order parabolic equationsof the form \[ Hu =\sum_{i,j=1}^ma_{ij}(x,t) X_iX_ju - \p_tu = 0, \(x,t)\in\R^{n+1}_+, \] where $X=\{X_1,...,X_m\}$ is a system of $C^\infty$vector fields in $\Rn$ satisfying H\"ormander's finite rank condition\eqref{frc}, and $\Omega$ is a non-tangentially accessible domain with respectto the Carnot-Carath\'eodory distance $d$ induced by $X$. Concerning thematrix-valued function $A=\{a_{ij}\}$, we assume that it be real, symmetric anduniformly positive definite. Furthermore, we suppose that its entries $a_{ij}$be H\"older continuous with respect to the parabolic distance associated with$d$. Our main results are: 1) a backward Harnack inequality for nonnegativesolutions vanishing on the lateral boundary (Theorem \ref{T:back}); 2) theH\"older continuity up to the boundary of the quotient of two nonnegativesolutions which vanish continuously on a portion of the lateral boundary(Theorem \ref{T:quotients}); 3) the doubling property for the parabolic measureassociated with the operator $H$ (Theorem \ref{T:doubling}). These resultsgeneralize to the subelliptic setting of the present paper, those in Lipschitzcylinders by Fabes, Safonov and Yuan in [FSY] and [SY]. With one proviso: inthose papers the authors assume that the coefficients $a_{ij}$ be only boundedand measurable, whereas we assume H\"older continuity with respect to theintrinsic parabolic distance.

Non-divergence form parabolic equations associated with non-commuting vector fields: Boundary behavior of nonnegative solutions