Continual fine-tuning of large language models (LLMs) suffers from catastrophic forgetting. Rehearsal-based methods mitigate this problem by retaining a small set of old data. Nevertheless, they still suffer inevitable performance loss. Although training separate experts for each task can help prevent forgetting, effectively assembling them remains a challenge. Some approaches use routers to assign tasks to experts, but in continual learning, they often require retraining for optimal performance. To address these challenges, we introduce the Sequential Ensemble of Experts (SEE) framework. SEE removes the need for an additional router, allowing each expert to independently decide whether a query should be handled. The framework employs distributed routing, and during continual fine-tuning, SEE only requires the training of new experts for incoming tasks rather than retraining the entire system. Experiments reveal that the SEE outperforms prior approaches, including multi-task learning, in continual fine-tuning. It also demonstrates remarkable generalization ability, as the expert can effectively identify out-of-distribution queries, which can then be directed to a more generalized model for resolution. This work highlights the promising potential of integrating routing and response mechanisms within each expert, paving the way for the future of distributed model ensembling.