National Natural Science Foundation of China [61202011, 61272152, 61033003, 91130034, 61320106005]; Ph.D. Programs Foundation of Ministry of Education of China [20120121120039, 20120142130008]; Natural Science Foundation of Hubei Province [2011CDA027] ; Spiking neural P systems with weights (WSN P systems, for short) are a class of distributed parallel computing devices inspired from the way neurons communicate by means of spikes. It has been proved that WSN P systems can generate/recognize Turing computable set of numbers (i.e., they are Turing universal as number generators/recognizers). In this work, we investigate the language generation power of WSN P systems, where the set of spike trains of halting computations of a given WSN P system constitutes the language generated by that system. Several relationships of the families of languages generated by WSN P systems with the family of finite languages and the family of regular languages are obtained. The family of recursively enumerable languages is characterized by projections of inverse-morphic images of languages generated by WSN P systems. (C) 2014 Elsevier Inc. All rights reserved.