Music genre classification remains a fundamental yet challenging task in music information retrieval, requiring models that capture local time--frequency patterns and long-range temporal dependencies. To address this, we propose ResMamba, a hybrid architecture that augments a ResNet-style four-stage backbone with Mamba blocks. Building upon the selective structured state space sequence model, ResMamba first adapts the selective SSM into a 4D-compatible residual Mamba block that captures global dependencies at linear complexity. We then design the ConvMamba dual-path block, which combines this adapted Mamba branch with a parallel convolutional branch through a learned $1\times1$ fusion, jointly modeling global sequential context and local spectro-temporal patterns. Furthermore, we adopt a multi-scale fusion head that aggregates hierarchical representations across all four stages. Experiments on the GTZAN dataset demonstrate that our full ResMamba model achieves a 5-fold cross-validation accuracy of $88.99\% \pm 1.58\%$, surpassing the strongest published method in our comparison (88.64\%). All models are trained from scratch without any pretraining, external data, or data augmentation. Beyond GTZAN, ResMamba also generalizes to the larger FMA benchmarks under the same training protocol, attaining $64.52\% \pm 1.88\%$ on FMA-Small under 10-fold cross-validation --- the best published from-scratch result --- and $65.75\%$ on FMA-Medium under the official artist-level split, surpassing the widely cited SVM baseline of Defferrard \textit{et al.} (63\%).

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