A device (D) is dedicated to the processing of application notifications that must be transmitted to users' communication terminals (TC) via at least one transmission infrastructure (RC). This device (D) comprises processing means (MT) configured, whenever an application notification intended for at least one user is received, to analyze that application notification so as to determine adaptation information which defines i) how and at what time that application notification's content must be transmitted to a chosen terminal (TC) of that recipient user, ii) what portion of the content must be used by that chosen terminal (TC), and iii) how that portion must be used by the chosen terminal (TC), depending on the chosen rule(s) and/or policy(-ies) and taking into account user and/or contextual information and/or the application notification's parameter(s) and/or characteristic(s) of the chosen terminal, and furthermore, to adapt the application notification to be transmitted based on the determined adaptation information.