High-resolution optical and near-infrared images of the centers of barred galaxies often show smaller, secondary bars within the main bar. A recent survey of 38 barred S0 and Sa galaxies shows bars-inside-bars to be surprisingly common: at least one quarter of the sample is double-barred. Some galaxies also show kiloparsec-scale inner disks, and nuclear rings. These central stellar structures suggest that the inner regions of early-type barred galaxies can be dynamically cool and disklike. The inner bars appear randomly oriented with respect to the main outer bar, suggesting that the two rotate independently.

How would the stars and gas orbit in a periodically-changing gravitational potential? I will discuss how one can characterize orbits in the double-bar system, and show how the technique is used to find the shapes and boundaries of circumstellar and circumbinary disks in an arbitrarily eccentric binary system.