Context. According to the current cosmological paradigm, large scale structures form hierarchically in the Universe. Clusters of galaxies grow through a continuous accretion of mass, and the presence of cluster substructures can be interpreted as signature of this process. Nevertheless, the rate and manner of mass accretion events are still matters of debate. Aims: We have analysed the presence of substructures in one of the largest sample of nearby cluster galaxies available in the literature. We have determined the fraction of clusters with substructure and the properties of the galaxies located in such substructures. Methods: Substructure in the galaxy clusters was studied using the Dressler-Shectman test, which was calibrated through extensive Monte Carlo simulations of galaxy clusters similar to real ones. In order to avoid possible biases in the results due to differing incompleteness among clusters, we selected two galaxy populations: a) galaxies brighter than Mr = -20 located in clusters at z < 0.1 (EC1); and b) galaxies of brightness Mr < -19 located at z < 0.07 (EC2). Results: In the inner cluster regions (r < r200) 11% and 33% of the clusters of EC1 and EC2 respectively show substructure. This fraction is larger in the outer cluster regions (≈ 55%) for EC1 and EC2 samples. Cluster global properties, such as σ_c, fb or Δ m12 do not depend on the amount of cluster substructure. We have studied the properties of individual galaxies located in substructures in the EC1 and EC2 galaxy populations. The fraction of galaxies within substructures is larger in the outer cluster regions when fainter galaxies are included. The distribution of relative velocities of galaxies within substructures suggest that they consist of an infalling population mixed with backsplash galaxies. We can not rule out that the infalling galaxy population located in substructures are genuine field ones.