I have a tab control contains two tabs, one shows me the messages of a running process and the other shows me a web page!
I have three buttons (start, stop and clear
You could use the CompositeCommand from the Prism Framework. Create an additional CompositeCommand in your viewmodel, register both ordinary commands with this CompositeCommand and bind the button to the CompositeCommand.
See the Prism documentation on page 130 on how to work with CompositeCommands.
Your app needs to reference Microsoft.Practices.Prism.dll which is included in the Prism package.