We report on a BeppoSAX observation of the transient X–ray pulsar 4U 0115+63 close to periastron . This led to the discovery of a dramatic luminosity variation from \sim 2 \times 10 ^ { 34 } erg s ^ { -1 } to \sim 5 \times 10 ^ { 36 } erg s ^ { -1 } ( factor \lower 2.15 pt \hbox { $ \buildrel > \over { \sim } $ } 250 ) in less than 15 hr . The variation was accompanied by only minor ( if any ) changes in the emitted spectrum and pulse fraction . On the contrary an observation near apastron detected the source in a nearly constant state at a level of \sim 2 \times 10 ^ { 33 } erg s ^ { -1 } . Direct accretion onto the neutron star surface encounters major difficulties in explaining the source variability properties . When the different regimes expected for a rotating magnetic neutron star subject to a variable inflow of matter from its companion are taken into consideration , the results of BeppoSAX observations of 4U 0115+63 can be explained naturally . In particular close to apastron , the regime of centrifugal inhibition of accretion applies , whereas the dramatic source flux variability observed close to periastron is readily interpreted as the transition regime between direct neutron star accretion and the propeller regime . In this centrifugal transition regime small variations of the mass inflow rate give rise to very large luminosity variations . We present a simple model for this transition , which we successfully apply to the X–ray flux and pulse fraction variations measured by BeppoSAX .