Except Naxat had nothing to do with the Crushes (except pressing and publishing, of course)... 
Compile developed and programmed the Crush games.
I have no idea who actually designed and programmed Psychosis, but I'd love to find out. It's possible Naxat did it in-house, I suppose.
Strange...Moby Games claims it was Naxat, as does Wikipedia. Of course, Wikipedia also says Compile developed them, so there goes that credibility.
Anyway, regarding Psychosis, it was apparently developed by Dual Corporation. At least, according to Moby Games.
http://www.mobygames.com/browse/games/dual-corporation/
EDIT: Upon further research, it looks like Alien Crush and Devil's Crush were co-developed by Compile and Naxat. So perhaps we're both right? Maybe. So says the internet. So who the hell knows?
MobyGames is full of shit, so is Wikipedia.
It's fairly common knowledge the Crush games were developed entirely by Compile, although if you need proof I can probably dig up about 5,343,284,783 sources for you. RED Company played some role (how big a role is unknown) in concept design for Devil's Crush, but the game was still ultimately drawn, composed and coded exclusively by Compile.
Naxat is/was a publishing house for the most part, if not exclusively. I'm not aware of any games Naxat played a part in developing off the top of my head, but that's not to say there aren't any.
Naxat and Compile had a long-running partnership where Compile would handle development while Naxat handled pressing and publishing. This union eventually became known as "Nazac," which is not only an obvious play on the the Naxat and Compile labels, but an anagram of Compile's first shooter "Zanac."
The moral of the story here is don't rely on what you see on the title screen for information on who developed a game. The copyright holder is almost always the publishing house and in many cases the developer is not even listed. The title screen for Blazing Lazers says "(C) 1989 Hudson Soft" but BL is just yet another Compile developed title. You don't even find this out until the final credit scroll after you beat the game.
I wouldn't be surprised to see an extensive article appear somewhere in the not too distant future that clarifies a lot of these points.
