[en] The magnetic properties of CePtAl with orthorhombic TiNiSi-type chemical structure were investigated. Single-crystal experiments of electrical resistivity, specific heat and magnetic susceptibility reveal the existence of three magnetic phase transitions at T₁ = 5.9 K (second order), T₂ = 4.3 K (first order) and T₃ = 2.2 K (first order). Powder neutron diffraction measurements detected complex magnetic structures consisting of two coexisting, partly incommensurate magnetic propagation vectors: k₁=0 and k₃=(0, 0.463(8), 0) for T₂≤T≤T₁; and k₁=0 and k₂ = (0, 1/2, 0) for T≤T₂. The predominantly ferromagnetic k₁ component and the antiferromagnetic k₂ component of the magnetic low-temperature structure of CePtAl were refined at 1.5 K. Magnetism in CePtAl is dominated by a ferromagnetic component (1.35(4) μ_B at 1.5 K) oriented parallel to the magnetically easy a axis. The complexity of magnetic structures in CePtAl appears to be caused by competing anisotropic magnetic exchange interactions in a network, where Ce-Ce nearest neighbours (3.56 AA) form chains parallel to the b axis and Ce-Ce second-nearest neighbours (3.77 AA) form chains along the a axis. (author)