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We present a deep Very Large Telescope (VLT) photometry in the regions surrounding the two dominant galaxies of the Antlia cluster, the giant ellipticals NGC 3258 and NGC 3268. We construct the luminosity functions of their globular cluster systems (GCSs) and determine their distances through the turn-over magnitudes. These distances are in good agreement with those obtained by the SBF method. There is some, but not conclusive, evidence that the distance to NGC 3268 is larger by several Mpc. The GCSs colour distributions are bimodal but the brightest globular clusters (GCs) show a unimodal distribution with an intermediate colour peak. The radial distributions of both GCSs are well fitted by de Vaucouleurs laws up to 5 arcmin. Red GCs present a steeper radial density profile than the blue GCs, and follow closely the galaxies' brightness profiles. Total GC populations are estimated to be about 6000 ± 150 GCs in NGC 3258 and NGC 4750 ± 150 GCs in NGC 3268. We discuss the possible existence of GCs in a field located between the two giant galaxies (intracluster GCs). Their luminosity functions and number densities are consistent with the two GCSs overlapping in projection., Facultad de Ciencias Astronómicas y Geofísicas, Instituto de Astrofísica de La Plata