Open the Terminal in the Utilities folder and enter or paste the appropriate command line. Press RETURN and enter your admin password when prompted. It will not be echoed.
To turn them ON: sudo tmutil enablelocal
To turn them OFF: sudo tmutil disablelocal
Note that turning them OFF will also delete all existing snapshots.
Local backups are automatically deleted under two circumstances.
1. Turn off Time Machine. (just turn it off between syncs, and then on again when you sync.)
2. When you sync (if left on)
There is not too much worry about space consumed, since the OS treats the files as low priority, and will delete them automatically if any other operation requires it.
There is also a Terminal Command to stop Local Backups.
EDIT: Yep, Kappy gave you the command.
Thank you. Will I then be able to enter time machine when I am home and connected to the external archive disk?
I ask you this beacuse when I've tried to disable local back ups with the tweak lion app, I could no longer enter time machine not even from my external disk...
Thank you for your help, be patient: I am a newbie (only switched to mac few months ago)
Sure. Removing the local snapshots only impact on when those backups were made because the computer was not connected to your Time Machine drive at the scheduled time. When disabled you Time Machine backups will only occur when the backup drive is hooked up.
I can't comment on the tweak lion app, whatever that was, but I would avoid such things unless you've tested them thoroughly. Perhaps that app is doing something other than it should. But before you disable snapshots per my post run that tweak app and disable the option so that the system is returned to what it should be.