One of Thunderbolt's features is that it contains both the PCI-express and DisplayPort protocols, which conveniently allows the mixing of both displays and other devices on the same daisy chain. In addition, because Thunderbolt contains DisplayPort, it should also be compatible with existing DisplayPort displays, such as Apple's 27-inch Cinema Display that was available before its Thunderbolt Display was released. Because of this a number of people who have been using Apple's DisplayPort-based Cinema Display have looked forward to using the monitor in a dual-display setup with Apple's new Thunderbolt Display, but unfortunately this will not work.
On paper, the use of DisplayPort and Thunderbolt monitors together appears as though it should work. After all, the criteria all fit together: besides the MacBook Air, Apple's other Thunderbolt-equipped Macs support up to two additional displays through the Thunderbolt connection, and the Thunderbolt specification allows a DisplayPort monitor to be the last device on the daisy chain.
Despite this, according to a recently released knowledge base article, if you connect your DisplayPort monitor to a Thunderbolt monitor, you will apparently not get any video output to it. Unfortunately Apple does not elaborate on exactly why this is the case, but it may be due to a limitation of the DisplayPort monitor itself. It is likely that while Thunderbolt supports up to two DisplayPort channels, a DisplayPort-only monitor does not and will therefore not be passed any video data if it is on the same chain as another monitor device.
This is an unfortunate development for people with current monitors who were hoping to create a dual-display setup with a Thunderbolt Display; however, so far it appears to be the only full limitation of Thunderbolt. Beyond this warning, Apple only suggests to get the best performance with a Thunderbolt Display, you should connect it to the computer as the first device, before other devices you may have. If you have purchased two Thunderbolt Displays, then place them in series as the first two devices in the chain.
reading•Apple outlines some Thunderbolt limitations
May 25•Samsung owes Apple $539M for infringing iPhone patents, jury finds
May 24•Valve accuses Apple of rejecting Steam Link mobile streaming app
May 24•iPhone 6 'bendgate' was real -- and Apple knew about it, according to court docs
May 23•Apple and Volkswagen joining forces to make autonomous shuttles, report claims