An important principle of theoretical cooperation of pragmatics was put forward by philosopher Herbert Paul Grice. But the principle of conversation cooperation itself was not perfect. Later, the theory "principle of politeness" of British linguist Geoffrey N. Leech had been suggested as the supplement and addition to it. But everyday's conversations are still often against both principles of in going communication situations. This article is a research on how these two principles can effect English conversations. And put forward a suggestion on how to solve these violations. Correct coordination using both principles on carry out Greetings and Conversation, which would make sure that people's linguistic communication will be carried out normally, smoothly, and most effectively.