Twelve drivers from the RMT union have walked out on the first of three strike days planned on Southern services.
The RMT claimed Southern had been forced to admit they were cancelling trains despite a promised full service.
Southern said there were cancellations following non-availability of crew owing to sickness and a rota mistake.
"There have been one or two cancellations this morning involving the non-availability of train crew, but these have arisen from one case of sickness and a train crew rostering error," a Southern spokesman said.
Southern has been in a long-running dispute over guards' roles on trains with the RMT, which represents conductors and 12 drivers, and Aslef, the main train drivers' union.
Aslef had planned three days of strike action this week but called off the stoppages for talks to take place.
The RMT continued with the walkouts after it said it was banned from negotiations.
As the 12 RMT drivers continued with the action, union leader Mick Cash called on Aslef to respect RMT picket lines, mounted at sites including the Barnham, Brighton and Selhurst depots.
Southern told the BBC all Aslef drivers crossed picket lines.
The RMT claimed it had seen a "positive response" to the protests but did not comment further.
Aslef said it could not comment on any ongoing Southern dispute while talks were under way.
Mr Cash said: "RMT is a recognised union for drivers on Southern and it is disgraceful that we have been carved out of the current talks process set up by the TUC and the government. That is a kick in the teeth for our members.
"All parties should be at the negotiating table."
Parent firm Govia Thameslink last week announced a fresh driver recruitment campaign on Southern, which has about 1,000 drivers.
Proposals by Chris Philp, the Conservative MP for Croydon South, to limit strike action and protect people's "right to get to work" have been rejected by MPs.
Mr Philp was denied permission to introduce his Industrial Action (Protection of Critical National Services) Bill to the House of Commons for further debate by 206 votes to 127.
A rail company has said roster errors and staff sickness are to blame for cancelled trains, not a strike by a dozen drivers.