[en] For a sequence of constant amplitude cyclic loading containing overloads, we propose a method for damage cumulation in non proportional loading. This method uses as data cyclic stabilized states at non proportional loading and initiation or fatigue curve in uniaxial case. For that, we take into account the dependence of Cyclic Strain Stress Curves (C.S.S.C.) and mean cell size on prehardening and we define a stabilized uniaxial state cyclically equivalent to a non proportional stabilized state through a family of C.S.S.C. Although simple assumptions like linear damage function and linear cumulation is used we obtain a sequence effect for difficult cross slip materials as 316 stainless steel, but the Miner rule for easy cross-slip materials. We show then differences between a load-controlled test and a strain controlled test: for a 316 stainless steel in a load controlled test, the non proportional loading at each cycle is less damaging than the uniaxial one for the same equivalent stress, while the result is opposite in a strain controlled test. We show also that an overloading retards initiation in a load controlled test while it accelerates initiation in a strain controlled test. (author). 26 refs., 8 figs