Class-Incremental Learning (CIL) with pre-trained models (PTMs) aims to sequentially adapt PTMs to new categories without forgetting old knowledge. Built upon PTMs, existing adapter-based methods mainly train models via distinct task-specific adapters, and present a uniform knowledge allocation for each adapter during inference. However, this allocation mechanism ignores the nature of task discrepancy and leads to suboptimal utilization of adapters. Also, under CIL constraint, an allocator is prone to forgetting when tasks evolve. To address these issues, we propose a Non-Forgetting Allocation with Bi-Level Competition (NoFA-BC). NoFA-BC constructs a non-forgetting allocator (NFA) by transforming the allocator training into a recursive least-squares problem and achieves an allocator equivalent to that trained with all data. Based on the NFA, a Bi-Level Competition (BLC) including an intra-task level Winner-Takes-All (WTA) mechanism and inter-task Last-Ones-Fall (LOF) elimination is proposed to provide better allocation of adapter knowledge. WTA extracts the most significant logit within a task to represent the adapter's contribution and LOF suppresses the irrelevant adapters. With BLC, participation ratio of each adapter can be tailored for each input. Moreover, a Stability Enhancement (SE) process is incorporated to further improve the performance of old tasks.