Abstract. -The mesoscopic one-dimensional magnetic texture caused by small Zeeman coupling in a p-wave superconductor in the magnetic field is found. The field orientation is opposite on the two sides of the texture and the magnitude can be even smaller than Hc1. The texture is not built from various singular topological defects, like vortices, as previously found in the simplest three-component Ginzburg-Landau model of superconductors.Introduction. -The order parameter in many classes of superconductors including organics of the type of Bechgaard salts [1], unconventional [2] and multiband superconductors [3] like heavy fermions or SrRuO, generally has several components. It describes coexisting condensates of Cooper pairs. The symmetry of the order parameter in unconventional superconductors is related to the crystallographic symmetry group of the material, the structure of the Fermi surface and the nature of the pairing mechanism. Although the number of charged fields and their transformation properties under rotations are different in any case, the common feature of theories describing these diverse systems remains the U (1) local gauge invariance. In systems of this kind, in the presence of an external magnetic field the major role is played by various topological defects. It is well known that, while in the simplest case, that of the one-component order parameter, the Abrikosov vortices (AV) are the only kind of topological defects, in the multicomponent case other types of defects exist.Machida [4] argued that in the p-wave superconductors with weak spin-orbit coupling the triplet pairing function can be represented by a three-dimensional complex vector field. The simplest Ginzburg-Landau model describing heavy fermion UPt 3 , even subjected to an external magnetic field B under condition of negligible Zeeman coupling, has an approximate SO(3) symmetry making it more amenable (and interesting) to mathematical analysis. This model was subsequently studied in more detail and various topologically distinct "non-Abrikosov" defects with sophisticated structure were found: coreless magnetic skyrmions [5,6], field-carrying