Abstract. The convex hull of n independent random points chosen on the boundary of a convex body K ⊂ R d according to a given density function is a random polytope. The expectation of its i-th intrinsic volume for i = 1, . . . , d is investigated. In the case that the boundary of K is sufficiently smooth, asymptotic expansions for these expected intrinsic volumes as n → ∞ are derived.