When introducing new angelfish into an existing tank of fish, you don't want any more conflicts than necessary. We've seen a lot of people suggest to move ornaments and decorations around to confuse the existing fish and prevent fighting. In our experience that seldom works with angelfish.
It is best to quarantine the new fish and start the introduction after it has recovered from it's trip and change in water. The first thing to do is to put a divider in the tank you're moving them to. The existing inhabitants are likely to be very territorial, regardless of their age or sex. Territorial aggression is the biggest threat to new fish. This is a situation where newly introduced fish are in danger of being seriously injured or killed. The divider will allow the new fish to get used to the tank and establish their own territories. You can buy a divider or make one from "egg crate" or even better, a foam divider that can double as a filter. After a couple weeks, it is generally safe to slightly move the divider to allow fish to swim to the other side. After a few days of this, it is probably okay to remove it completely. Just be prepared to put it back if there is any serious fighting.
Another technique is to introduce all the fish to a tank at once. If you are getting fish from different sources, it's best to quarantine each source separately and then after the quarantine period, put them all into the community tank at the same time. This way, there will be no territorial aggression at the beginning.
There is a common misconception that it's best to introduce fish of the same size. The thought being that they can defend themselves easier. We've found that it doesn't work very well. It's best to introduce new fish that are much larger or much smaller. Much larger fish can usually fend for themselves. Much smaller fish are often chased for a few minutes and then ignored after the large fish realize they can't catch them and that they're no threat. We've often times use small angelfish as dither fish for pairs. The pairs seldom are able to harm them and we find ourselves quickly looking for more tank-space as these "dither" fish do so well and grow so fast in those situations. In many instances the dither fish grew into the dominant fish in the tank over time.
We hope some of these hints aid in your successful introduction of newly acquired angelfish.
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