The EuFe2-xNixAs2 compounds exhibiting 3d and/or 4f magnetic order were investigated by means of 57Fe and 151Eu Mössbauer spectroscopy. Additionally, results for the end members of this system, i.e. EuFe2As2 and EuNi2As2, are reported for comparison. It was found that spin-density-wave order of the Fe itinerant moments is monotonically suppressed by Ni-substitution. However, the 3d magnetic order survives at the lowest temperature up to at least x = 0.12 and it is certainly completely suppressed for x = 0.20. The Eu localized moments order regardless of the Ni concentration, but undergo a spin reorientation with increasing x from the alignment parallel to the a-axis in the parent compound, toward c-axis alignment for x > 0.07. The change of the 4f spins ordering from antiferromagnetic to ferromagnetic takes place simultaneously with a disappearance of the 3d spins order what is the evidence of a strong coupling between magnetism of Eu2+ ions and the conduction electrons of [Fe2-xNixAs2]2- layers. The Fe nuclei experience the transferred hyperfine magnetic field due to the Eu2+ ordering for Ni-substituted samples with x > 0.04, while the transferred field is undetectable in EuFe2As2 and for compound with a low Ni-substitution level. It seems that the 4f ferromagnetic component arising from a tilt of the Eu2+ moments to the crystallographic c-axis leads to the transferred magnetic field at the Fe atoms. The superconductivity is not observed down to 1.8 K, although a comparison with 57Fe and 151Eu Mössbauer data for EuFe2As2-based superconductors indicates a similar magnetic structure.