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A variant of membrane computing models called Spiking Neural P systems (SNP systems) closely mimics the structure and behavior of biological neurons. As third-generation neural networks, SNP systems have flexible architectures allowing the design of bio-inspired machine learning algorithms. This paper proposes Modular Spiking Neural P (MSNP) systems to solve image classification problems, a novel SNP system to be applied in scenarios where hundreds or even thousands of different classes are considered. A main issue to face in such situations is related to the structural complexity of the network. MSNP systems devised in this work allow to approach the general classification problem by dividing it in smaller parts, that are then faced by single entities of the network. As a benchmark dataset, the Oxford Flowers 102 dataset is considered, consisting of more than 8000 pictures of flowers belonging to the 102 species commonly found in the UK. These classes sometimes present large variations within them, may be also very similar to one another, and different images of the same subject may differ a lot. The work describes the architecture of the MSNP system, based on modules focusing on a specific class, their training phase, and the evaluation of the model both concerning result accuracy as well as energy consumption. Experimental results on image classification problems show that the model achieves good results, but is strongly connected to image quality, mainly depending on the frequency of images, remarkable changes of pose, images not centered, and subject mostly not shown. [ABSTRACT FROM AUTHOR]