Talks are taking place between rail union RMT and Southeastern Trains after more than 750 station platform staff and guards voted to strike.
Guards on Southeastern Trains are among those who voted to strike
More than 400 platform workers voted by six to one for action over cuts in the number of station staff on duty.
Some 350 guards also voted to strike over manning levels at Hastings, Ramsgate and Dover Priory Stations.
Southeastern said it was disappointed with the strike vote and hoped talks could resolve the dispute.
The company, which is owned by Govia, took over running trains in Kent, East Sussex and south-east London on 1 April.
The services had previously been run by government subsidiary South Eastern Trains after Connex lost the franchise in 2003.
The RMT wanted the region's train services to be kept under public sector control, arguing reliability had improved under South Eastern.
It claims the new staffing levels will put staff and passengers at greater risk of attacks.
"The travelling public wants to see more staff on stations, not fewer, and our members have the right to work in safety," said general secretary Bob Crow.