A support point bearing device for a pulley arm is configured in such a manner that a sleeve (7) is inserted into a shaft hole (5) in a boss section (4) which is provided to the pulley arm (1), washers (8) are fitted over the respective outer peripheries of small-diameter cylinder sections (7a) which are formed at both ends of the sleeve (7), and the sleeve (7) is affixed to an engine block (30) by tightening a bolt (20) which is inserted through the sleeve (7), thereby allowing the pulley arm (1) to be supported in a rotatable manner. Seal receiving recesses (11) having a large diameter are provided in both ends of the shaft hole (5), and circular cylinder sections (12a) which are provided to the outer peripheral sections of seal members (12) are press-fitted into the seal receiving recesses (11). Radial lips (12c) which tilt inward are provided on the inner peripheries of the seal members (12), and the tips of the radial lips (12c) are brought to be in elastic contact with the outer diameter surface of the sleeve (7). The radial lips (12c) are adapted so that, when inner pressure has increased, the radial lips (12c) elastically deform in the direction in which the diameter of the radial lips (12c) reduces, and consequently, the contact pressure of the radial lips (12c) relative to the outer diameter surface of the sleeve (7) is increased.