Quantum chemical calculations are applied to complexes of 6‐OX‐fulvene (X=H, Cl, Br, I) with ZH3/H2Y (Z=N, P, As, Sb; Y=O, S, Se, Te) to study the competition between the hydrogen bond and the halogen bond. The H‐bond weakens as the base atom grows in size and the associated negative electrostatic potential on the Lewis base atom diminishes. The pattern for the halogen bonds is more complicated. In most cases, the halogen bond is stronger for the heavier halogen atom, and pnicogen electron donors are more strongly bound than chalcogen. Halogen bonds to chalcogen atoms strengthen in the order O