Let ▫$\gamma(G)$▫ be the domination number of a graph ▫$G$▫. It is shown that for any ▫$k \ge 0$▫ there exists a Cartesian graph bundle ▫$B \Box_\varphi F$▫ such that ▫$\gamma(B \Box_\varphi F) = ...\gamma(B)\gamma(F) - 2k$▫. The domination numbers of Cartesian bundles of two cycles are determined exactly when the fibre graph is a triangle or a square. A statement similar to Vizing's conjecture on strong graph bundles is shown not to be true by proving the inequality ▫$\gamma(B \boxtimes_\varphi F) \le \gamma(B)\gamma(F)$▫ for strong graph bundles. Examples of graphs ▫$B$▫ and ▫$F$▫ with ▫$\gamma(B \boxtimes_\varphi F) < \gamma(B)\gamma(F)$▫ are given.
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