Solution:

one fish, one cat and one dog.



Explanation:

The question might appear a bit difficult in the starting but if you analyze the statements, you will realize that it is just a tricky one.



All except two were fishes and all except two were cats. With these statements we can assume that two of the animals were not fishes and two were not cats. Now one of those animals that are not fishes can be a cat and one of those two animals that are not cats can be a fish. Just carry out the same analysis for the statement that all except two animals were not dogs and you will come across the result i.e.:

In that competition, there was one fish, one cat and one dog.