The T&G said it is recommending acceptance of the offer from SPT
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Union officials have recommended acceptance of a revised pay and conditions offer to striking staff on the Glasgow Underground.
The T&G union said the Strathclyde Passenger Transport offer "greatly improves the basic rate for all T&G members working at Glasgow Subway".
The union said pledges on shifts and career progression were also included in the SPT offer.
Underground bosses said they now hoped further stoppages would be called off.
Details of the proposals have not been released ahead of next week's vote.
Dan Sharpe, T&G Scotland's regional industrial organiser, said: "The revised offer greatly improves the basic rate of all our members - drivers, station masters and assistants.
'Unanimously recommended'
"It takes into account counter-proposals from T&G shop stewards to make shifts more family friendly and a career structure for station masters, and a commitment by the employer to view sympathetically job evaluation.
"It is our intention to meet with our members as early as possible next week and the offer will be unanimously recommended for acceptance by our negotiating committee."
SPT said the talks with the union had been "productive" and it hoped another stoppage planned to start next Friday would be called off while the union puts the new offer to its members.
The action has led to a series of stoppages of the underground system. The latest was a four-day stoppage which began last Friday.