CoNi/Ni multisegmented cylindrical nanowires were synthesized via an electrochemical route. The wires are 140 nm in diameter, with 1000 nm long Ni segments and CoNi segments between 600 and 1400 nm in length. The magnetic configuration was imaged by XMCD-PEEM in the demagnetized state and at remanence after magnetizing axially and perpendicularly. Ni segments, with cubic crystal symmetry, show an axial magnetic configuration with a small curling component at the surface. In turn, CoNi segments, with hexagonal crystal symmetry and a strong magnetocrystalline anisotropy perpendicular to the nanowires, show a single vortex state in the shorter segments and multivortex or multitransverse magnetic configurations in medium and long segments, respectively. A detailed study by micromagnetic simulations reveals that the magnetic configuration is determined mainly by the coupling between soft Ni and harder CoNi segments. For short CoNi segments, Ni segments are magnetostatically coupled and the chirality of the single vortex formed in CoNi remains the same as that of the curling in neighboring Ni segments. For longer CoNi segments, the remanent state is either the multivortex or multitransverse state depending on whether the previously applied field was parallel or perpendicular to the magnetocrystalline axis. The results point out the relevance of the cylindrical geometry to promote the occurrence of complex magneto-chiral effects and provide key information for the design of cylindrical magnetic nanowires for multiple applications.