Process running for several minutes in Sleep mode My Mac OS is OS X Yosemite (Version 10.10.2).

Normally I put the mac in Sleep mode before going to bed, and I realize very often that the machine starts to run in the night just for several minutes and then back to silence.

I guess there is some bad process/software in my Mac that wakes up the system from time to time.

I know that Activity Monitor could check processes, but I have no idea how to see what is wrong...

Could anyone help?
As of OS X Mountain Lion (10.8), there has been a feature called "Power Nap" that allows the Mac to periodically wake from sleep while connected to a power adapter to retrieve emails, calendar updates, iCloud syncing, or to back up to Time Machine. This would be my guess for the reason why your Mac is waking up and running during the night and not an indication of a bad process on your Mac.

If this is unwanted behavior, it's an easy setting to switch off in System Preferences > Energy Saver: 



Note that another option here is "Wake for network access" - which would be along the lines of remote or local file/printer sharing while in sleep. I would doubt this is happening since you are asleep yourself while it's occurring :-)