DNA sequencing and several other applications of single- molecule detection (SMD) currently under development utilize spectroscopic measurements for categorization of different types of fluorophores. In the collection and analysis of data from such experiments, the photon signals are sorted into different channels, depending upon their arrival time, emission wavelength, or other distinguishable properties. If the photon statistics are adequate, maximum-likelihood estimation (MLE) techniques can be successfully applied to determine which fluorophore is present. However, data analysis using neural network (NN) methods can offer several advantages. We consider data from a Monte Carlo simulation of SMD in a flow-cell, in which a time-resolved fluorescence decay profile is accumulated for each photon burst. A 2-layer NN, with sigmoid as the activation function, is trained on a set of simulated data using back-propagation and the (delta) - learning rule, and then used for identification of photon bursts in subsequent simulations. The NN is able to consider additional input parameters, such as the amplitudes of the weighted-sliding-sum digital-filter output of the photon bursts and the durations of the bursts. It can yield superior identification of photon bursts, particularly in cases where the fluorophores have disparate fluorescence quantum efficiencies, absorption cross-sections, or photodegradation efficiencies, or where the categorization includes other possibilities, such as background fluctuations, or the simultaneous presence of both fluorophores.