Abstract: tThis study shows how road traffic networks events, in particular road accidents on blackspots, can bemodelled with simple probabilistic distributions. We considered the number of crashes and the numberof fatalities on Spanish blackspots in the period 2003-2007, from Spanish General Directorate of Traf-fic (DGT). We modelled those datasets, respectively, with the discrete generalized Pareto distribution(a discrete parametric model with three parameters) and with the discrete Lomax distribution (a dis-crete parametric model with two parameters, and particular case of the previous model). For that, weanalyzed the basic properties of both parametric models: cumulative distribution, survival, probabilitymass, quantile and hazard functions, genesis and rth-order moments; applied two estimation methodsof their parameters: the _ and (_ + 1) frequency method and the maximum likelihood method; usedtwo goodness-of-fit tests: Chi-square test and discrete Kolmogorov-Smirnov test based on bootstrapresampling; and compared them with the classical negative binomial distribution in terms of absoluteprobabilities and in models including covariates. We found that those probabilistic models can be usefulto describe the road accident blackspots datasets analyzed.