A transaction will not be included in the blockchain unless the address(es) that are funding it have a confirmed balance equal to or above the input amount. You can see many transactions here that are funded with unconfirmed coins
Here - (bitcoincharts.com - warning-10MB web page). Just search for "1dice" and you will see that "Satoshi Dice" is paying out with unconfirmed coins (creating possibly 1000+ transactions that will never complete).
If the second transaction uses an input address with no previous balance, then it will remain pending until the first transaction (that pays adequate funds to that address) is included in the blockchain.