The concept of cooperation and distribution as known from grammar systems is introduced to spiking neural P systems (in short, SN P systems) in which each neuron has a finite number of sets (called components) of rules. During computations, at each step only one of the components can be active for the whole system and one of the enabled rules from this active component of each neuron fires. The switching between the components occurs under different cooperation strategies. This paper considers the terminating mode, in which the switching occurs when no rule is enabled in the active component of any neuron in the system. By introducing this new mechanism, the computational power of asynchronous and sequential SN P systems with standard rules is investigated. The results are that asynchronous standard SN P systems with two components and strongly sequential unbounded SN P systems with two components are Turing complete. © Springer International Publishing Switzerland 2014.