Polymerization of ethylene optionally with 1-olefins involves polymerizing ethylene in presence of a catalyst in gas-phase reactor (1) to form polymer particles and reaction gas containing propane, circulating unpolymerized ethylene to remove the heat of polymerization, and separating propane fraction in second separation stage and using for degassing polymer particles discharged from reactor such that the partial pressure of ethylene in propane fraction used for degassing is less than 6000 Pa and that of 1-olefins and 4-12C alkanes in propane fraction is less than 10000 Pa. Polymerization (p1) of ethylene optionally with further 1-olefins involves polymerizing ethylene in the presence of a catalyst in a gas-phase reactor (1) to form polymer particles and reaction gas containing propane, circulating unpolymerized ethylene to remove the heat of polymerization, discharging the polymer particles (dis)continuously from the reactor, separating the polymer particles from the major part of the concomitantly discharged gas and degassing them, freeing the gas of entrained fine particles, separating the gas from a low-boiling fraction containing ethylene or from a high boiling fraction containing further 1-olefins or 4-12C alkanes in a first separation stage, and separating a propane fraction in a second separation stage and using it for degassing the polymer particles discharged from the reactor. The partial pressure of ethylene in the propane fraction used for degassing is less than 6000 Pa and the partial pressure of the sum of further 1-olefins and 4-12C alkanes in the propane fraction is less than 10000 Pa. Independent claims are included for the following: (1) an apparatus for carrying out the process (p1) comprising: a gas-phase reactor (1) containing a bed of polymer particles, a recycle gas line (3) connected to the reactor for carrying away and recirculating the reaction gas comprising propane and unpolymerized ethylene.