Shifting cron job

Is there a way to set up cron job to be ran at intervals of one hour and one minute? E. g. 12:00, 13:01, 14:02, 15:03 and so on indefinitely. When it gets again at 12 hours it should execute job at 12:24, the next at 13:25.

Try the at command.

at +61m < commands.list

commands.list: doupdate.sh at +61m < commands.list

Of course, you want to use the full path for your files. Each time this runs, it will set up the next job 61 minutes in the future.

You can run "atq" to view what is currently queued up.

Check out fcron which is available with most distros and is more suitable for this kind of task.