The local density of states (DOS) in the quantum-well region of a double-barrier resonant-tunneling structure is calculated for the case of zero applied bias. As the barrier potential ${V}_{0}$ goes to zero, the local DOS approaches an ${E}^{1/2}$ behavior; as ${V}_{0}$ goes to infinity, a staircaselike local DOS is obtained. A one-dimensional DOS, characterized by a fixed momentum transverse to the barriers, goes like ${E}^{\mathrm{\ensuremath{-}}1/2}$ as ${V}_{0}$ goes to zero and like a series of \ensuremath{\delta} functions in the limit of infinite ${V}_{0}$. The behavior of these local-DOS functions is examined for physically realizable structures.