When they first meet, Gwendolen and Cecily get on very well together. Gwendolen immediately announces her certainty that they are "going to be great friends" and Cecily replies:
How nice of you to like me so much after we have known each other such a comparatively short time.
They continue in this amicable vein until it emerges that they are both engaged to marry Ernest Worthing. It is at this point that they become rivals and antagonists. The tone of both becomes notably frosty as they argue over which of them has the best claim to him. They attempt to restrain their rancor while Merriman is serving tea, but even then their comments to one another continue to be barbed.
When Jack and Algernon enter, it is quickly established that the two men to whom they are engaged are, in fact, different people and that neither of them is called Ernest. Shocked by this betrayal, Gwendolen and Cecily return to being on good terms with one another, and this time they remain so since they are not, in fact, in competition with one another for a husband.
In Act 3, they are briefly united in their stand against Jack and Algernon then forgive them at the same time. Their views on every subject, particularly that of the desirability of a man being named Ernest, unite them and seem to cement their friendship very quickly.