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This paper develops local learning algorithms to solve a classification task with the help of biologically inspired mathematical models of spiking neural networks involving the mechanism of spike‐timing‐dependent plasticity (STDP). The advantages of the models are their simplicity and, hence, the potential ability to be hardware‐implemented in low‐energy‐consuming biomorphic computing devices. The methods developed are based on two key effects observed in neurons with STDP: mean firing rate stabilization and memorizing repeating spike patterns. As the result, two algorithms to solve a classification task with a spiking neural network are proposed: the first based on rate encoding of the input data and the second based on temporal encoding. The accuracy of the algorithms is tested on the benchmark classification tasks of Fisher's Iris and Wisconsin breast cancer, with several combinations of input data normalization and preprocessing. The respective accuracies are 99% and 94% by F1‐score. [ABSTRACT FROM AUTHOR]