In this paper, we study simultaneous shrinking target problems in the nonautonomous dynamical systems induced by Cantor series expansions. Let \(Q=\{q_{k}\}_{k\ge 1}\) be a sequence of positive integers with \(q_{k}\ge 2\) for all \(k\ge 1\) . Put \(T_{Q}^{n}(x)=q_{1}\cdots q_{n}x-\lfloor q_{1}\cdots q_{n}x\rfloor \) for each \(n\ge 1\) , which gives the Q-Cantor series expansion. Let \(Q_1=\{q_{1,k}\}_{k\ge 1},Q_2=\{q_{2,k}\}_{k\ge 1}\) be two sequences as aforesaid and \(\varphi _1,\varphi _2:\mathbb {N}\rightarrow \mathbb {R}^{+}\) be two positive functions. We determine the Lebesgue measure of the set \(\begin{aligned} \left\{ (x,y)\in [0,1]^2:\begin{aligned}&|T^n_{Q_1}(x)-x_0|<\varphi _1(n) \\ &|T^n_{Q_2}(y)-y_0|<\varphi _2(n) \end{aligned}~\text {{i.o.}}\right\} , \end{aligned}\) where \(x_0,y_0\in [0,1]\) and i.o. stands for infinitely often. Let \(f_1,f_2:[0,1]\rightarrow [0,1]\) be two Lipschitz functions and \(\tau _1,\tau _2:[0,1]\rightarrow \mathbb {R}^{+}\) be two positive continuous functions. We determine the Hausdorff dimension of the set \(\begin{aligned} \left\{ (x,y)\in [0,1]^2:\begin{aligned}&|T^n_{Q_1}(x)-f_1(x)|<(q_{1,1}\cdots q_{1,n})^{-\tau _1(x)} \\ &|T^n_{Q_2}(y)-f_2(y)|<(q_{2,1}\cdots q_{2,n})^{-\tau _2(y)} \end{aligned}~\text {{i.o.}}\right\} . \end{aligned}\) At the same time, the Hausdorff dimension of the set \(\begin{aligned} \left\{ (x,y)\in [0,1]^2:\begin{aligned}&|T^n_{Q_1}(x)-g_1(x,y)|<(q_{1,1}\cdots q_{1,n})^{-\tau _1(x)} \\ &|T^n_{Q_2}(y)-g_2(x,y)|<(q_{2,1}\cdots q_{2,n})^{-\tau _2(y)} \end{aligned}~\text {{i.o.}}\right\} \end{aligned}\) is also determined, where \(g_1,g_2:[0,1]^2\rightarrow [0,1]\) are two Lipschitz functions.
