The focus is on the G6 alliance, which needs to compete with matching slot costs with the P3 mega alliance and its mega ships if it is to enjoy similar economies of scale.
One leading shipbroker said in its latest monthly bulletin that contracts for ships of both 14,000 TEU and 18,000 TEU may be signed in the latter part of the year.
Hapag-Lloyd executive board member Ulrich Kranich has spoken of acquiring 18,000-TEUers "sooner or later", and that every member of the alliance "must be thinking about ships of that size".
Hapag's merger partner CSAV's chief financial officer Nicolas Burr said the two lines were devising a big investment programme, seeking to gain something like P3 slot costs.
MOL president Toshiya Konishi said the G6 Alliance would likely to have two loops of 18,000 TEUers by 2020 or shortly after.
"We are always looking for options and studying but have not yet made any decision," he said.
"Perhaps we'll have a maximum of two sets of 18,000 - 19,000 TEU ships by 2020, or by 2022 or 2023. It's a long-term issue," said Mr Konishi.
P3 carriers Maersk, MSC and CMA CGM are the only lines in an alliance to possess mega ships in such quantities. China Shipping and United Arab Shipping Co are the only other lines with 18,000-TEUers on order.
A resurgence of investment in very large containerships as global carriers strive to catch up with the few that have already ordered 18,000-TEU ships could unsettle the market, brokers warn.