The following from the ICAO North Atlantic MNPS Manual, presume the same procedures apply on the southern oceanic routes,
Chapter 11: Special Procedures for In-Flight Contingencies
11.1 INTRODUCTION
11.1.1 The following procedures are intended for guidance only. Although all possible contingencies cannot be covered, they provide for such cases as:
• inability to maintain assigned level due to weather (for example severe turbulence);
• aircraft performance problems; or
• pressurisation failure.
11.1.2 They are applicable primarily when rapid descent, turn-back, or diversion to an alternate aerodrome is required. The pilot's judgement will determine the specific sequence of actions taken, having regard to the prevailing circumstances.
11.2 GENERAL PROCEDURES
11.2.1 If an aircraft is unable to continue its flight in accordance with its ATC clearance, a revised clearance should be obtained whenever possible, prior to initiating any action, using the radio telephony distress (MAYDAY) signal or urgency (PAN PAN) signal as appropriate.