Help! My Tetras are eating each other?

Yesterday,I bought 5 Neon Tetras to add to my fish tank.I already have 6 black/blue Tetras ( Not sure what specie ) , 4 flag tetras and one orange tetra im not sure about either.They all get along fine.When I added the fish and woke up today,2 were dead with barely any scales.My other tetras were nibbling on them,also,1 other tetra was alive but hardly moving and my other tetras were taking bites outta him.My other two are OK for the moment,but they hardly swim that much either.What's wrong? My other tetras have never fought before.