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In $L_2({\mathbb R}^d;{\mathbb C}^n)$, we consider a selfadjoint operator${\mathcal B}_\varepsilon$, $0< \varepsilon \leqslant 1$, given by thedifferential expression $b({\mathbf D})^* g({\mathbf x}/\varepsilon)b({\mathbfD}) + \sum_{j=1}^d (a_j({\mathbf x}/\varepsilon) D_j +D_j a_j({\mathbfx}/\varepsilon)^*) + Q({\mathbf x}/\varepsilon)$, where $b({\mathbf D}) =\sum_{l=1}^d b_l D_l$ is the first order differential operator, and $g, a_j, Q$are matrix-valued functions in ${\mathbb R}^d$ periodic with respect to somelattice $\Gamma$. It is assumed that $g$ is bounded and positive definite,while $a_j$ and $Q$ are, in general, unbounded.  We study the generalized resolvent $({\mathcal B}_\varepsilon - \zetaQ_0({\mathbf x}/\varepsilon))^{-1}$, where $Q_0$ is a $\Gamma$-periodic,bounded and positive definite matrix-valued function, and $\zeta$ is acomplex-valued parameter. Approximations for the generalized resolvent in the$(L_2 \to L_2)$- and $(L_2 \to H^1)$-norms with two-parametric error estimates(with respect to the parameters $\varepsilon$ and $\zeta$) are obtained.

Two-parametric error estimates in homogenization of second order elliptic systems in $\mathbb{R}^d$ including lower order terms