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In this paper, we report on a considerable (up to about 18%) magnetoresistance (MR) effect in glass-coated Co-Cu microwires prepared from immiscible elements. Samples of Co10Cu90 microwires with a metallic nucleus diameter of 3-17 μm and total diameter up to 25 μm were prepared by the Taylor-Ulitovsky technique. The Co10Cu90 microwires generally consist of nanocrystals of Co and Cu with average grain size of about 40 nm, although the Co-phase content depends on the microwire geometry (metallic nucleus radius and glass-coating thickness). The magnetic field dependence of MR is completely anhysteretic, showing monotonous decay with the magnetic field.