The study is devoted to heavily drawn multicore Cu–18Nb composites of cylindrical and rectangular shapes. The composites were fabricated by the melt-and-deform method, namely, 600 in situ rods of Cu–18%Nb alloy were assembled in a copper shell and cold-drawn to a diameter of 15.4 mm (e = 10.2) and then rolled into a rectangular shape the size of 3 × 5.8 mm (e = 12.5). The specimens were analyzed from the viewpoints of their microstructure, microhardness, and thermal stability. The methods of SEM, TEM, X-ray analysis, and microhardness measurements were applied. It is demonstrated that, at higher strain, the fiber texture 110Nb∥ 111Cu∥ DD (drawing direction), characteristic of this material, becomes sharper. The distortions of niobium lattice can be observed, namely, the 110 Nb interplanar distance is broadened in longitudinal direction of specimens and compacted in transverse sections. The copper matrix lattice is distorted as well, though its distortions are much less pronounced due to its recrystallization. Evolution of microstructure under annealing consists mainly in the coagulation of ribbon-like Nb filaments and in the vanishing of lattice distortions. The structural changes in Nb filaments start at 300–400 °C, then develop actively at 600 °C and cause considerable decrease of strength at 700–800 °C.