In crystals of La2CuO4.02 oxygen diffusion can be limited to such small length scales, that the resulting phase separation is invisible for neutrons. Decomposition of the 139 La NQR spectra shows the existence of three different regions, of which one orders antiferromagnetically below 17 K concomitantly with the onset of a weak superconductivity in the crystal. These regions are compared to the macroscopic phases seen previously in the title compound and the cluster-glass and striped phases reported for the underdoped Sr-doped cuprates.PACS numbers: 74.72.Dn, 75.30.Ds, 75.40.Gb Inhomogeneous carrier and spin distributions in high-T c compounds might be related to phase separation and stripes, 1,2 and are intensively studied especially in hole doped La 2 CuO 4 . In underdoped La 2−x Sr x CuO 4 for x > 0.06 doping leads to spin-density wave order or stripe formation, as seen by neutron scattering at various x-values. 3-6 Recent NQR and NMR studies have revealed new interesting features, like line intensity suppression caused by spin/charge fluctuations, stripe condensation at low temperatures under favorable pinning conditions, and the presence of inequivalent copper sites attributed to a stripe formation. 7-10 At very low Sr content (x < 0.02) the magnetic properties are explained in terms of hole segregation, 11-14 and the formation of a cluster spin glass (x=0.06). 15 For La 2 CuO 4+x the presence of the mobile oxygen dopants leads to a macroscopic structural phase separation in antiferromagnetic (AF) and superconducting (SC) regions in the concentration range 0.01 < x < 0.06 (the so called miscibility gap). [16][17][18] The oxygen mobility is linked to lattice imperfections, e.g. it is strongly increased by the presence of planar defects. 19 In La 2 CuO 4+x single crystals prepared by the molten solution method 20 oxygen mobility is very low due to the small number of defects and hence the scale of the structural separation can be minimized. The single crystal with x = 0.02 prepared by this way appears homogeneous below 200 K in X-ray and neutron studies, 21 although the composition is inside the miscibility gap. In the crystal a superconducting transition is observed around 15-17 K with a very weak diamagnetic signal. 21,22 According to µSR 21 part of the sample becomes magnetically ordered below the same temperature of 15 K, but neutron diffraction does not see any long range magnetic structure. Apparently phase separation happens, but the scale is too small to be visible by standard structural methods. 21 By performing NQR on the same La 2 CuO 4.02 single crystal, we will demonstrate the existence of three regions with different oxygen concentrations and show only one (oxygen-poor) phase to have an antiferromagnetic transition. We evaluate the size of the antiferromagnetic regions from the reduction of staggered magnetization. By comparison with the macroscopic phases seen previously in the title compound 17 and the clusterglass and striped phases seen in La 1.94 Sr 0.06 CuO 4 and La 2−x−y Sr x Eu y CuO...