The nonequilibrium delta(non)-phase was originally investigated in the work[1] when studying the ageing processes of the 1424 alloy (Al-Li-Mg-system). As shown in the work[2] this phase may also be formed during the cooling from the temperature of SSHT. The delta(non)-phase precipitates are also present in 1420 alloy of the same system[3]. The basic structure investigations were carried out on the 1424 alloy sheets aged in accordance with the regime: 125 degrees C, 32 hrs. The investigations were performed by TEM using the JEOL JEM 200CX microscope. The diffraction patterns from the delta(non)-phase on the crystallographic axes of zones close to < 110 >, < 111 >, < 112 > were obtained. It can be seen that the regular reflex networks appeared after the deviation from axes of zones by 3-4 degrees. It was established that the lattice parameters of delta(non)-phase and its orientation relation with the matrix can be approximately described by the following way: a(delta non) approximate to a(alpha)/2[112] b(delta non) approximate to a(alpha)/2[1 (1) over bar0] C-delta non approximate to a(alpha) [11 (1) over bar] where a(alpha)- the period of the FCC- lattice of solid solution. The model of the crystallographic structure of the delta(non)-phase precipitates is proposed. On the basis of this model the mechanism of the delta(non)-phase formation is discussed. The late ageing stages are analyzed and it was shown that the km-phase particles are the nuclei for S-1(Al2LiMg)- phase.