Max and Rocky frequently chase each other around. It seems to be mostly a game for them, especially Max. She likes to grab his tail. He is mostly indifferent towards her, but will defend himself if necessary. As always, we watch them closely. Also, since they are of similar size and can fly, we allow this. If they were of vastly different size -- for example, if Rocky were a large macaw -- this type of play would not be allowed at all.
In this first video, Rocky had been playing in the hallway, happily alone. Max flew down and wanted to play with him. He tried to get away from her, which turned it into a game.
In this second video, the two of them were under the kitchen table (mess under the table due to the fact that the parrots had been loose much of the day -- it was all swept up before we went to bed.) Then, when Rocky sees me trying to make a video, everything takes a (not so surprising) turn.