Vision-Language Models (VLMs) have demonstrated remarkable zero-shot capabilities, yet adapting them for continual learning while preserving these abilities remains challenging. The fundamental challenge lies in addressing dual forgetting: backward forgetting (catastrophic forgetting of previously learned tasks) and forward forgetting (degradation of pre-trained zero-shot capabilities during task-specific adaptation). Current approaches face significant limitations: prompt-based methods achieve parameter efficiency but suffer from limited plasticity under domain shifts, while mixture-of-experts (MoE) approaches provide adaptive capacity but require extensive iterative optimization. To address this dual forgetting challenge, we propose Ridge Regression-based Analytic Adaptation with Mixture of Experts (R \(^2\) A \(^2\) -MoE), a framework that enables collaborative specialization through ridge regression-based expert learning. Our key contribution is the introduction of collaborative analytical experts that decompose continual adaptation into specialized closed-form optimization problems, enabling both representational flexibility and computational efficiency. Extensive experiments on X-TAIL and MTIL benchmarks demonstrate that R \(^{2}\) A \(^{2}\) -MoE achieves competitive performance while significantly reducing computational overhead—decreasing parameter count by 45.59%, GPU memory usage by 56.27%, and training time by 46.21% compared to existing MoE-based methods. Our results indicate that collaborative analytical specialization provides a promising direction for efficient continual learning in vision-language models.