This week's book giveaway is in the OO, Patterns, UML and Refactoring forum. We're giving away four copies of Refactoring for Software Design Smells: Managing Technical Debt and have Girish Suryanarayana, Ganesh Samarthyam & Tushar Sharma on-line! See this thread for details.
You can use redirect. Do whatever processing that you need to do in your first servlet and then you can redirect the control to your second servlet (by specifying the URL) and then complete the remaining processing.