Abstract We have investigated the magnetism of CoCrFeNiZr x (x = 0.4–0.5) eutectic high-entropy alloys (HEAs) in relation to their microstructure by XRD, SEM, magnetization, specific heat and electrical resistivity measurements. Two structural phases develop in the CoCrFeNiZr x HEAs, a Zr-free fcc solid solution and a Zr-containing C15 Laves-phase intermetallic compound, where in both phases magnetic transition elements Co, Cr, Fe and Ni substitute each other in a random-like manner. Relative fractions of the two phases change substantially with the Zr concentration. Microstructurally, the two phases form alternatively grown fine lamellar structure typical of eutectic alloys. In addition, bulky dendrites of the fcc solid solution form in large number for the x = 0.40 concentration and in small number for x = 0.45. Two magnetic structures coexist in the CoCrFeNiZr x HEAs. The first is a disordered ferromagnetic (FM) phase that develops in the interior of large dendrites of the fcc solid solution and in some larger lamellas of this phase. The second phase is superparamagnetic-like and originates from the remaining spins of the fcc solid solution fraction, located at the surfaces and in the interfaces, and from all spins of the C15 Laves-phase fraction. The relative magnitude of the disordered FM-state magnetization with respect to the superparamagnetic magnetization in the samples with different Zr concentration is predominantly determined by the volume fraction of the fcc bulky dendrites. There is no one-to-one relation between the two magnetic structures on one side and the two structural components of the CoCrFeNiZr x eutectic mixtures on the other side. The magnetism of multi-phase HEAs containing magnetic elements cannot be described as a compositional average of magnetic properties of the constituent phases.