Q:

what if two logrotate run concurrently

I know this sounds weird...
I have a project which will run "logrotate myConf.conf" automatically every hour.
Besides, in my cron/, there is also a logrotate running...
The two process might have chance to modify the same log file
In this case what will happen?
Will the log file be totally screwed? or just one of the command will fail? (which is good enough)

A:

Yes, there may be issues relating to the state file that logrotate keeps.
See my answer to a question about a corrupt state file due to concurrent runs of logrotate from cron:

/var/lib/logrotate/status gets invalid entries

The summary: be sure that your specific rotation job is either run as part of the system's ordinary rotation job, or run it from a personal cron job and use a separate state file (specified with the -s option to logrotate). I either case, only run the rotation from one cron job.

