RMT union members at Northern Rail began a 48-hour walkout on Monday morning, affecting services to Yorkshire destinations including Leeds, Sheffield, Bradford, Hull, Skipton, York and Harrogate.
The train operator ran 550 services in a revised timetable yesterday, plus some additional journeys after a number of conductors decided to come to work as normal.
Bosses said a revised timetable would be in place again today.
The strike action does not affect services run by other train companies in the North.
Northern Rail managing director Ian Bevan said: "Despite the RMT strike action we are covering about 40 per cent of our network and expect to carry tens of thousands of passengers."
Another RMT strike affected rail services elsewhere in the country, as drivers for Arriva Trains Wales held a 24-hour stoppage over pay and conditions.
The action followed a strike on the London Underground on Boxing Day, which caused disruption on every Tube line. Members of the drivers' union Aslef walked out over a claim for triple pay and a day off in lieu.
London district organiser Steve Grant said members had shown "100 per cent" support for the walkout, claiming that the union had tried to negotiate.
But London Underground managing director Mike Brown said union leaders had shown "complete disdain" for passengers hoping either to visit friends and family at Christmas or to pick up bargains in the sales.
The strike was criticised by London Mayor Boris Johnson, who accused the union of "trying it on", adding: "The demands being made by the leadership of Aslef are monstrous.
"It has been clear ever since the Gregorian calendar was reformed in the mid-18th Century that Boxing Day 2010 would fall on a Sunday.
"So why do they demand more money with three weeks to go?"