This thesis proposes a novel feature selection and classification method employing evolving spiking neural networks (eSNN) and evolutionary algorithms (EA). The method is named the Quantum-inspired Spiking Neural Network (QiSNN) framework. QiSNN represents an integrated wrapper approach. An evolutionary process evolves appropriate feature subsets for a given classification task and simultaneously optimises the neural and learning-related parameters of the network. Unlike other methods, the connection weights of this network are determined by a fast one-pass learning algorithm which dramatically reduces the training time. In its core, QiSNN employs the Thorpe neural model that allows the efficient simulation of even large networks. In QiSNN, the presence or absence of features is represented by a string of concatenated bits, while the parameters of the neural network are continuous. For the exploration of these two entirely different search spaces, a novel Estimation of Distribution Algorithm (EDA) is developed. The method maintains a population of probabilistic models specialised for the optimisation of either binary, continuous or heterogeneous search spaces while utilising a small and intuitive set of parameters. The EDA extends the Quantum-inspired Evolutionary Algorithm (QEA) proposed by Han and Kim (2002) and was named the Heterogeneous Hierarchical Model EDA (hHM-EDA). The algorithm is compared to numerous contemporary optimisation methods and studied in terms of convergence speed, solution quality and robustness in noisy search spaces. The thesis investigates the functioning and the characteristics of QiSNN using both synthetic feature selection benchmarks and a real-world case study on ecological modelling. By evolving suitable feature subsets, QiSNN significantly enhances the classification accuracy of eSNN. Compared to numerous other feature selection techniques, like the wrapper-based Multilayer Perceptron (MLP) and the Naive Bayesian Classifier (NBC), QiSNN demonstrates a competitive classification and feature selection performance while requiring comparatively low computational costs.