the field~marginal distributions of the Wigner function!. The application of this procedure to determine the Wigner function of squeezed states of light has been very successful experimentally @11#. Other methods, also leading to the indirect determination of the Wigner function @12# or of the density matrix @13# through measurements of auxiliary quantities, have been proposed by several groups @14#. More recently, it was shown that the Wigner function of an electromagnetic field in a cavity or the vibrational state of a trapped ion could be directly measured, by a simple experimental procedure @15#, which yields a physical meaning to that phase-space distribution, and eliminates the need of applying integral transforms to marginal distributions. Since this proposal for the direct measurement of the Wigner function was based on specific properties of the two systems considered, it is a nontrivial matter whether that idea could be extended to other systems. In this paper, we show that the Wigner function of the vibrational state of a molecule can also be directly measured. Our proposal is based on the same expression for the Wigner distribution as the one in @15#. The physics is, however, quite different, the specificities of the molecular system playing an important role in the present scheme. Other methods for reconstructing the state of molecular vibrations have been suggested in Refs. @16,17#, including the case of anharmonic vibrations @17#. In the next section, we introduce the Wigner function for a molecular vibrational state, and express it in a convenient form, on which our further developments are based. In Sec. III, we describe the method for measuring directly the Wigner function of a molecular vibrational state. In Sec. IV, we discuss possible experimental procedures, and compare our proposal with other approaches. In Sec. V we simulate numerically a realization of the proposed method. Finally, in Sec. VI, we summarize our discussions.