The zero degree calorimeters (ZDCs) for the ALICE experiment will measure the energy of the spectator nucleons in heavy ion collisions at the CERN LHC. The dipole magnets of the LHC beam optics will separate the ion beams from the spectator protons; the spectator protons and neutrons will be respectively detected by the proton (ZP) and the neutron (ZN) calorimeters. Since all the spectator nucleons have the same energy, the calorimeter response is proportional to their number, providing a direct information on the centrality of the collision. ZDCs are spaghetti calorimeters, which detect the Cherenkov light produced by the shower particles in silica optical fibers embedded in a dense absorber. The technical characteristics of ZP and ZN detectors are described. The calorimeters have been tested at the CERN SPS using pion and electron beams with momenta ranging from 50 to 200 GeV/c; the ZN detector behaviour has also been studied with an indium beam of 158 GeV/c per nucleon. The beam test results are presented: the calorimeters response, the energy resolution and the localizing capability. Also the signal uniformity and a comparison between the transverse profile of the hadronic and electromagnetic shower are discussed. Moreover the differences between the ZP detector responses to protons and pions of the same energy have been investigated, exploiting the proton contamination in the positive pion beams.