Monitors are doing strange things

I'm running an iMac with a Thunderbolt 2nd Monitor. A wonderful setup until recently (I think about the time I upgraded to High Sierra. Problems began when the Thunderbolt monitor would go blank. I would get it back by unplugging the power cord, then plug it back in. More recently, when I turn on my iMac in the morning, both monitors are blank. I get them to come back after two or three restarts. Today, one screen covered both monitors, but no Dock or menus at the top. Getting concerned. Could this be a High Sierra problem?