Both the larger versions of the Dreamliner and the A350 are already undergoing flight tests.
The new 777-X could carry close to 400 passengers, the Dreamliner 330 and the A350 could seat around 366 passengers. Air New Zealand's 777-200s seat 312 passengers. The aircraft sell for between US$312 million to US$400m.
Luxon, who was at the International Air Transport Association's annual meeting, said his airline would continue to target the Australian market who wanted to fly to North or South America via Auckland.
While it will be hunting for new large aircraft, the smaller new generation A320 family aircraft it has ordered have been delayed.
The A320/21 New Engine Option planes were due for delivery later this year but will now not arrive for another 11 months.
Problems scaling up production of the Pratt and Whitney engines have been blamed.
Air New Zealand will buy or lease 13 of the aircraft that would be used on Australian and Pacific Island routes.
Luxon said although the NEOs would give efficiency of up to 15 per cent, there would be no significant impact on its bottom line.
''If we can take some time out and it's 11 months then we can help let the engine programmes mature. There are just some durability issues that they need to hunt down,'' he said.
''We've learned how to deal with aircraft delays - the Dreamliner was four and half years late.''
The delay allowed the plane maker to redesign the interior and install more seats. There would be 214 seats, five more than the original configuration.
Airbus chief operating officer for customers, John Leahy, said during a media briefing in Cancun that the delay was unfortunate.
''The airframes are ready which is why some people go to Hamburg and see our glider fleet sitting there. It happens in the industry from time to time.''
• Grant Bradley travelled to Cancun with the assistance of IATA and Air New Zealand.