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Large language models (LLMs) excel at capturing global token dependencies via self-attention but face prohibitive compute and memory costs on lengthy inputs. While sub-quadratic methods (e.g., linear attention) can reduce these costs, they often degrade accuracy due to overemphasizing recent tokens. In this work, we first propose *dual-state linear attention* (**DSLA**), a novel design that maintains two specialized hidden states—one for preserving historical context and one for tracking recency—thereby mitigating the short-range bias typical of linear-attention architectures. To further balance efficiency and accuracy under dynamic workload conditions, we introduce DSLA-*Serve*, an online *adaptive distillation* framework that progressively replaces Transformer layers with DSLA layers at inference time, guided by a sensitivity-based layer ordering. DSLA-*Serve* uses a chained fine-tuning strategy to ensure that each newly converted DSLA layer remains consistent with previously replaced layers, preserving the overall quality. Extensive evaluations on commonsense reasoning, long-context QA, and text summarization demonstrate that DSLA-*Serve* yields **2.3×** faster inference than Llama2-7B and **3.0×** faster than the hybrid Zamba-7B, while retaining comparable performance across downstream tasks. Our ablation studies show that DSLA’s dual states capture both global and local dependencies, addressing the historical-token underrepresentation seen in prior linear attentions.