British Airways says about 90 percent of services will run as normal on Wednesday as the airline recovers from a two-day strike by pilots, report agencies.
However, BA said its full schedule would not be in place for "some time" as 150 aircraft and 700 pilots started the day "in the wrong place".
BA cancelled almost all its flights on Monday and Tuesday in a dispute over pay and conditions.
Another strike by pilots is planned for later this month.
BA said on Wednesday: "The nature of our highly complex, global operation means that it will take some time to get back to a completely normal flight schedule however, we plan to fly more than 90 percent of our flights today."
About half of the airline's 300 aircraft are out of position. And in addition to pilots being in the wrong place, BA said there was severe disruption to rosters for its 4,000 cabin crew.
The airline is offering affected customers refunds or the option to re-book to another date of travel or an alternative airline.
Balpa said that the strikes had been a "powerful demonstration of the strength of feeling of BA pilots".
Tens of thousands of flights had to be cancelled, costing BA an estimated £40m a day.
It called on the airline to come "back to the negotiating table with some meaningful proposals" to try to avert the next scheduled strike, on 27 September.
Balpa general secretary, Brian Strutton, said: "Surely any reasonable employer would listen to such a clear message, stop threatening and bullying, and start working towards finding a solution."
Pilots had previously rejected an 11.5 percent pay increase over three years proposed by BA in July.
Balpa says its members have taken lower pay rises and made sacrifices during more stringent times for the airline in recent years.
But it says that now BA's financial performance has improved - its parent company IAG reported a 9 percent rise in profits last year - they should see a greater share of the profits.
BA has said its pilots are already paid "world-class" salaries, and has described the pay offer as "fair and generous".
After three years of the proposed pay deal, some captains could be taking home more than £200,000 per year, including allowances, it said.
