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Spiking neural P systems with thresholds(SNPT systems) are a class of bio-inspired computing models,inspired by the association between the potential changes in neurons and the neural activities.It is proved that SNPT systems working in the maximally parallel mode are computationally universal since they can achieve the equivalent computation power with Turing machines as number generators and acceptors.The computing power of SNPT systems working in other modes is a topic of concern.In this work,we investigate the number generating power of SNPT systems working in the global asynchronous and local synchronous way(ASNP_locsynT systems).It is proved that ASNP_locsynT systems with integer weights are universal,and ASNP_locsynT systems with positive-integer weights can only generate the semilinear sets of numbers.The results show that the range of synaptic weights affects the computation power of ASNP_locsynT systems.