Zazumama

I have a male Congo African Grey who is now 1 1/2 years old. Approximately one month ago I was given an male Eclectus. He too is 1 1/2 years old. Their cages are in the same room and yes they see each other all the time. Often I will hold the Grey in my right hand and the Eclectus in the left hand, however, I have never put them together so they can interact with each other for fear that one might hurt the other. Neither one has ever showed aggression towards the other, but I'm still concerned. Does anyone have any suggestions as to how I might introduce them to each other?