  We study the behavior of the Eisenbud-Wigner collisional time delay around
Feshbach resonances in cold and ultracold atomic and molecular collisions. We
carry out coupled-channels scattering calculations on ultracold Rb and Cs
collisions. In the low-energy limit, the time delay is proportional to the
scattering length, so exhibits a pole as a function of applied field. At high
energy, it exhibits a Lorentzian peak as a function of either energy or field.
For narrow resonances, the crossover between these two regimes occurs at an
energy proportional to the square of the resonance strength parameter
$s_\textrm{res}$. For wider resonances, the behavior is more complicated and we
present an analysis in terms of multichannel quantum defect theory.
