Often in analyzing systems, the emulation of Replay Attack becomes important. Are systems that protected against CCA attacks also immune against replay attack, or it is a different criterion? Thanks
These are different - protection against a replay attack could for example be done by recording that a message was already handled or by including a timestamp in the message and not processing the message if it is too old.
Note that for a replay attack the attacker doesn't get the plaintext, but does get access to at least 1 previously sent message. In CCA the attacker doesn't not have access to previously sent messages, and can request back the plaintext for chosen ciphertexts.
Short: These are different.
CCA security usually refers to IND-CCA2 -- indistinguishable ciphertexts under adaptive chosen ciphertext attacks. This is a security notion for encryption schemes. This model does not consider any semantics / context of the messages that get encrypted.
As you probably know, resistance against replay attacks is a protocol property. It says that you cannot send the same message twice to trigger the same action again. This notion only makes sense when you consider the context of messages and how they are used. Note that you do not even need encryption to achieve this property!
So, these properties are really on different levels.