[en] The superfluid density for He₄ films adsorbed in two different geometries has been studied. With Vycor glass, using a third sound technique, phonons with a T₂ temperature dependence have been observed. These are attributed to the cylindrical nature of the Vycor pores. Also observed were rotons with a 5 K energy gap. The observations were in substantial agreement with calculations by Padmore and others for two-dimensional rotons. Also studied were He₄ films adsorbed in porous Vycor glass near their critical points using an Andronikashvili method. The superfluid density was found to vary as a power law in reduced temperature with an exponent equal to the bulk value. This three-dimensional critical behavior was attributed to the three-dimensional interconnectedness of the Vycor substrate. For He₄ films using a Mylar substrate with an Andronikashvili method, profound differences in the nature of the superfluid transition have been observed. A sharply changing superfluid density at the transition was seen along with a peak in the superfluid dissipation. By interpreting the data through a dynamic theory, the Kosterlitz-Thouless picture of superfluidity in two dimensions was supported. Good numerical agreement with the universal constant predicted by the theory was obtained