"behave like a normal" is a correct and usable phrase in written English.
You can use it when referring to someone who is acting abnormally or out of the ordinary. For example, "Please try to behave like a normal person".
He will likely become jealous when you behave like a normal person who talks to and interacts with others.
Let me behave like a normal person.
But Beuys did not behave like a normal artist, and that is what this photograph is saying.
He was a source of disappointment to his father, who nagged at Jim to behave like a normal boy.
I couldn't suddenly go down to the PEN Club and behave like a normal human being, because most of those guys were struggling to make a couple of thousand pounds a year".
And, as many people on the wrong side of the Cold War line used to say, the real opposition which 'They' cannot cope with is just to behave like a normal human being, to do an honest day's work, to be an ordinary mother or father at home and to say what an ordinary wife or husband would say.
If we are in denial and try to insist that our love one talk and behave like a 'normal' person, we will be miserable every time we see the person.
In the end, I wasn't behaving like a normal human being".
Doctors order him to return to Paris and start behaving like a normal person.
Over geological time, this oddity has allowed complex life to survive and evolve despite the Earth's successive ice ages, periods when fragile life forms would have otherwise been wiped out on the desiccated, frozen ground and – if water behaved like a normal liquid – in solidified seas, too.
The app behaves like a normal Web app, says Google, but it can use the new APIs like synchronization.
