Sensory stimuli typically activate many receptors at once and therefore should lead to increases in correlated activity among central neurons. Such correlated activity could be a critical feature in the encoding and decoding of information in central circuits. Here we characterize correlated activity in response to two biologically-relevant classes of sensory stimuli in the primary electrosensory nuclei, the ELL, of the weakly electric fish Apteronotus leptorhynchus. Our results show that these neurons can display significant correlations in their baseline activities that depend on the amount of receptive field overlap. A detailed analysis of spike trains revealed that correlated activity resulted predominantly from a tendency to fire synchronous or anti-synchronous bursts of spikes. We also explored how different stimulation protocols affected correlated activity: while prey-like stimuli increased correlated activity, conspecific-like stimuli decreased correlated activity. We also computed the correlations between the variabilities of each neuron to repeated presentations of the same stimulus (noise correlations) and found lower amounts of noise correlation for communication stimuli. Therefore, the decrease in correlated activity seen with communication stimuli is caused at least in part by reduced noise correlations. This differential modulation in correlated activity occurred because of changes in burst firing at the individual neuron level. Our results show that different categories of behaviourally relevant input will differentially affect correlated activity. In particular, we show that the number of correlated bursts within a given time window could be used by post-synaptic neurons to distinguish between both stimulus categories.