Multilayers of a Nb0.37Ti0.63 alloy, a chief material of superconducting magnet technology, and a Cu0.95Sn0.05 or Cu0.70Ni0.30 alloy exhibit a dimensional crossover with a decreasing bilayer period Λ=dN+dS, where dS=3dN. Cusps of Hc2(θ) and square root Hc2||(T) develop when Λ≤40 nm, which indicate a crossover to 2D behavior from 3D behavior seen at Λ=60 nm. Full proximity coupling of Cu–Sn layers for Λ=13 nm restores isotropic angular dependence, but with sharply lower Hc2 values. By contrast, proximity coupling was suppressed by magnetic Cu–Ni layers, and 2D behavior was retained while Tc fell below 4 K for Λ≪20 nm. The data are consistent with numeric results obtained by Takahashi and Tachiki [Phys. Rev. B 33, 4620 (1986)] when the variation of the Bardeen–Cooper–Schrieffer pairing potential is the primary cause of the dimensional crossover. Since practical Nb–Ti conductors have a layered nanostructure, this result suggests that a dimensional crossover should also be found in wires. However, the 3D–2D crossover occurs when Λ is much greater than the separation of the flux lines at high field (10–20 nm) and above the range where optimum flux pinning is found. This implies that a 2D state (for insulating or magnetic layers) or a 2D strongly coupled state (for normal metals) exists when flux pinni- ng is strongest. These implications are discussed in the context of practical Nb–Ti wires used in superconducting magnet technology. © 1999 American Institute of Physics.