The approximate intensity ratio 1:3 or 1:4 for the 4–0 and 3–0 vibrational bands of HD observed by Herzberg seems rather high on the basis of the usual anharmonicity considerations. To understand this, the problem is discussed qualitatively on the basis of classical mechanics. A quantum mechanical calculation of the intensities of various vibrational transitions is made by an extension of the perturbation theory treatment by Wick for the fundamental band. The relative intensities of the various vibrational bands are finally expressed as a function of the ratio ξ = a(0; 1)/a(0; 0) of the matrix elements, with respect to the vibrational states 1 and 0, of a quantity closely resembling the polarizability of the molecule. For the 4–0 and 3−0 bands, the intensity ratio I(4–0)/I(3–0) does not depend very much on the ratio ξ and has the value ~0.27, in agreement with the approximate observed value. The case of the molecular ion HD+ is also briefly discussed.