Some 200 so-called "apron control" staff - who direct aircraft in and out of their parking positions both in the control tower and on the tarmac - first walked out last Thursday, causing hundreds of flights, primarily domestic and short-haul, to be cancelled so far.
On Monday, Fraport, the company which owns and operates Europe's third-busiest hub, said that although 240 of a total 1,250 flights were cancelled, it had been able to ensure around 1,000 flights, or more than 80 percent, above all intercontinental connections.
Fraport said it hoped to make sure that a similar proportion of services take off and land on Tuesday.
According to documents made available by Fraport, the union is demanding pay rises of 25 to 50 percent, depending on a worker's grade, as well as increased bonuses and reduced working hours.
Frankfurt airport is Europe's third busiest after London-Heathrow and Paris Charles de Gaulle.
GdF repeatedly threatened strike action last year in a long-running wage dispute for regular air traffic controllers.
A strike was averted when the union and Germany's air safety authority DFS reached a deal in court in October.