The equation of state (EOS) of nuclear matter is discussed within the Brueckner‐Bethe‐Goldstone approach. First the energy per particleE/Ais calculated in the Brueckner‐Hartree‐Fock limit with the Argonnev18potential, using the continuous choice as auxiliary potential. Then, the contribution of three‐body clusters is determined by solving the Bethe‐Faddeev equation, and the equivalence with the same calculations based on the standard choice as auxiliary potential, is demonstrated. In spite of reaching a quite good convergence of the hole‐line expansion, the resulting EOS does not fit the empirical saturation density (&rgr;0= 0.17 fm−3). To this end, three‐body forces (TBF) are introduced. A first class of microscopic TBF comprises effects due toNN¯virtual excitations via &sgr; and &ohgr;‐meson exchanges (the main relativistic correction to Brueckner theory), the 2&pgr;‐exchange, and the virtual excitation of the lowest nucleonic resonanceN*(1440). We compare with a phenomenological TBF, involving two parameters adjusted on the saturation density and energy. Next, using microscopic or phenomenological TBF, the symmetry energy of nuclear matter is computed, allowing to determine the EOS of beta‐stable and charge neutral matter, and the properties of neutron stars, in particular the mass‐radius curve. © 2004 American Institute of Physics