The structural properties of purely siliceous and Al-substituted protonated gmelinite, a zeolite with a medium-sized unit cell, are investigated by means of first-principles local-density functional calculations. For acid sites introduced into an Al-free structure, optimized geometries are compared with experimental data. The substitution of a Si-O fragment by Al-O-H induces a pronounced local deformation of the structure. Four symmetrically distinct O sites (O-1-O-4) are classified, according to the pattern of the deformation, into two categories showing rather localized (sites 2 and 3), and mostly delocalized (sites 1 and 4) distortions. Relative stabilities of protonated structures are shown to depend on the initial geometry of the site. Larger Si-O-Si angles lead to a higher stability of the acid site. Two approaches, a static and a dynamical one, are used to derive OH stretching frequencies. Both of them prove a rather complex relation between the infrared (IR) frequency, the acidity, and the local environment of the Bronsted acid site. The lowest OH stretching frequency is assigned to the O-2 site as distinguished in the dynamical calculations. The shift occurs due to attractive interactions of H to the framework oxygen atoms.