A new statistical method for the estimation of the response latency is proposed. When spontaneous discharge is present, the first spike after the stimulus application may be caused by either the stimulus itself, or it may appear due to the prevailing spontaneous activity. Therefore, an appropriate method to deduce the response latency from the time to the first spike after the stimulus is needed. We develop a nonparametric estimator of the response latency based on repeated stimulations. A simulation study is provided to show how the estimator behaves with an increasing number of observations and for different rates of spontaneous and evoked spikes. Our nonparametric approach requires very few assumptions. For comparison, we also consider a parametric model. The proposed probabilistic model can be used for both single and parallel neuronal spike trains. In the case of simultaneously recorded spike trains in several neurons, the estimators of joint distribution and correlations of response latencies are also introduced. Real data from inferior colliculus auditory neurons obtained from a multielectrode probe are studied to demonstrate the statistical estimators of response latencies and their correlations in space.