Density functional (DF) calculations including gradient-exchange and correlation corrections have been performed on the LnH, LnO, and LnF series (Ln = La, Gd, Yb, and Lu). Relativistic first-order perturbations including S-O couplings are accounted for. The calculated molecular constants are in reasonable agreement with the experimental ones. The calculated lanthanide contractions of the three series, i.e. R(La-X) - R(Lu-X), are quite different, 0.19 Angstrom (0.19 Angstrom) for LnH, 0.10 Angstrom (0.11 Angstrom) for LnF, and only 0.05 Angstrom (0.04 Angstrom) for LnO. There is good agreement between the calculated values and the experimental ones (values in parentheses). This astonishing variation has two origins, a monoatomic and a diatomic one, which are related to each other. The first po;int is the noninteger 4f-shell population. Participation of unoccupied 4f-AOs in outer-valence shell bonding is important for strongly bound lighter lanthanides. The second point is the "rigidity" of the bond : the larger the bond energy or the force constant, the smaller the lanthanide contraction.