There are three types of ADRs: Level 1, 2, and 3. Due to meeting certain reporting requirements, a "Level 3" and a "Level 2" ADR could trade on a listing exchange such as NYSE and Nasdaq. A "Level 1" ADR offering is exempt from full SEC reporting requirements and will trade Over-the-Counter in the Pink or OTC markets due to it's minimal regulatory oversight.
An SEC Investor Bulletin with information regarding ADRs can be found by clicking here (scroll down to "What is an ADR?").