Typically, secure channels are constructed from an authenticated key exchange (AKE) protocol, which authenticates the communicating parties based on long-term public keys and establishes secret session keys. In this paper we address the partial leakage of long-term secret keys of key exchange protocol participants due to various side-channel attacks. Security models for two-party authenticated key exchange protocols have been developed over time to provide security even when the adversary learns certain secret values. This paper combines and extends the advances of security modelling for AKE protocols addressing more granular partial leakage of long-term secrets of protocol participants. Further, we fix some flaws in security proofs of previous leakage-resilient key exchange protocols.