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Abstract: Catastrophic forgetting is a fundamental challenge in sequential learning for artificial neural networks, particularly spiking neural networks (SNNs), which aim to emulate biologically plausible neuronal dynamics. In this study, we investigate the role of sleep-mediated replay in mitigating catastrophic forgetting during sequential task learning. We trained a multilayer SNN on two sequentially presented image classification tasks (Task A and Task B) using spike-timing-dependent plasticity (STDP) learning rules. During offline periods, we implemented spontaneous replay of Task A patterns to emulate biological sleep consolidation. Our results demonstrate that sleep-mediated replay keeps Task A performance (0.589 before Task B, 0.206 after sleep) while allowing effective acquisition of Task B (0.672 before sleep). In contrast, networks trained sequentially without sleep exhibit severe forgetting (Task A drops to 0.011 after Task B). These findings suggest that sleep-like replay mechanisms can enable continual learning in SNNs, providing a computationally and biologically grounded approach to memory consolidation. We further analyze synaptic weight distributions and firing rate dynamics, revealing that sleep stabilizes task-specific synaptic patterns without impeding new learning. This work bridges computational neuroscience and artificial intelligence, suggesting that sleep-like replay could be an effective approach for continual learning in SNNs.