Frank,
If you deleted a class file by hand, did you do it outside the workspace or within it? If outside, you need to Refresh that project by right-clicking on it and selecting ‘Refresh’ from its context menu.
Eclipse generally keeps all compilations up to date at all times. This behavior is controlled by the setting at ‘Window’ > ‘Preferences’ > ‘Workbench’ > ‘Perform build automatically on resource modification’.
Forcing a recompilation of an entire source tree is normall done by selecting the project in the Package Explorer view and choosing the menu item at ‘Project’ > ‘Rebuild Project’.