Artificial neural networks (ANNs) achieve remarkable results on various tasks, but understanding the computational mechanisms underlying their performance remains difficult. Furthermore, traditionally employed artificial networks have little in common with real biological networks. Overcoming this difference, machine-learning-based training methods for spiking neuronal networks (SNNs) have been developed to create functional networks, enabling the investigation of these neural networks with neuroscientific analysis methods. Here we analyze one such SNN trained with backpropagation based on a time-to-first-spike coding scheme to classify the MNIST dataset (98% accuracy, built on [1]), with the goals 1) to understand the mechanisms of the classification and 2) to get an inspiration about potential brain mechanisms. In response to the presentation of a sample, the network exhibits spiking activity, propagating through the layers in a feed-forward manner. We observe that in deeper layers more neurons are involved in the classification and their spikes get more synchronized. This behavior is reminiscent of the activity propagation in synfire chains (SFCs) [2]. These SFCs were proposed as a model for the transmission of information in the cortex [3, 4], expected to form distinct paths through a network enabling the separation of different stimuli [3]. We indeed identify such paths in the trained network. Neurons are preferentially active in response to samples of a particular class (e.g. different ‘1’s in the MNIST dataset). This preference becomes more distinct in the deeper layers of the network. This is complemented by the observation that these neurons have strong excitatory connections onto the correct output neuron. We also find that the timing of the activation of inhibitory and excitatory connections plays an important role: while in non-correct output neurons the activation timing of inhibition and excitation balances or inhibition even dominates, the correct output neuron is inhibited later. Summarizing, we show that the activity of this trained SNN can be understood as the propagation of specific excitation and non-specific inhibition. This relates to SFCs taking different paths through the network. These SFCs naturally emerge in this network through training without actively enforcing such a structure.