Marking a task as completed in Nozbe is done by simply clicking on the box to the left of the task..  Completed tasks are automatically grayed and sent to the bottom of the list.

Flagging Tasks as Complete

Clean Up Your Lists

If you mark tasks as completed instead of deleting them, periodically archive or delete old tasks to keep your lists trim.

CAUTION! Project – Next Step tasks are special. Re-process them when you see them, do NOT mark it as completed until you have re-processed it or the entire project is complete!