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In this paper we introduce a novel class of caches, named step caches, that can be used to implement concurrent memory access in shared memory multithreaded multiprocessor systems on chip (MP-SOC) without cache coherency problems. The main difference between ordinary caches and steps caches is that data entered to a step cache is kept valid only until the end of ongoing step of multithreaded execution. We describe the structure and operation of step caches as well as give a performance evaluation of step cache systems with different settings using simple parallel programs on our paramedical MP-SOC framework. According to the evaluation, step caches speed up execution by a factor close to the number of processors in respect to the similar system without step caches and almost achieve the performance of the ideal shared memory systems in plain concurrent access.