This work proposes a new scheme for the replacement of cache lines in computer systems. Performance of the proposed algorithm was tested by conducting simulation experiments. Several simulation models were developed for the cache and neural network paradigms. Our simulation engine was driven by traces from the real world workloads/benchmarks. The proposed strategy uses learning properties of non- estimating type of neural networks to understand the replacement phenomenon and guide the replacement decisions made by the cache controller. Therefore, the strategy was successful in being able to eliminate dead lines from the cache memory more efficiently as compared to the conventional algorithms. We observed from the simulation experiments that a well- designed non-estimating neural network- based replacement policy does provide excellent performance as compared to the overwhelmingly used LRU scheme. The new approach can be applied to the page replacement and prefetching algorithms in virtual memory systems.