More than 8,000 Unison and GMB members walked out on Tuesday in a 48-hour strike - believed to be the biggest of its kind.
Around 12,500 workers, mostly women, are proceeding with claims against the council following a Court of Session ruling last year.
The council said the strike was unnecessary and it hopes to reach a settlement in the coming months and start paying out in the next financial year.
Many strikers manned picket lines around the city on Tuesday and later joined a march from Glasgow Green to George Square for a rally, chanting “equal pay or we walk away”.
Glasgow City Council said all early years establishments, additional support for learning (ASL) schools and mainstream primary schools would be closed on both days, though all mainstream secondary schools would remain open.
Home care services for around 6,000 people are affected by the industrial action.
Workers on the picket line at The Mitchell Library hope the strike will put pressure on the council to speed up the negotiation process.
Anna Murray, a cleaning supervisor at the library who has worked there for 25 years, said: “We’ve waited 10 years for equal pay and the council doesn’t seem to be doing anything to pay it so we’ve gone out on strike in support of getting our equal pay paid.
“We hope that the council speed things up and gets equal pay for the people that are waiting for it.”
Annette Tompson, another cleaning supervisor at The Mitchell, where she has worked for 17 years, added: “It has been taking a long long time, we’ve been to the employment tribunal, to the court, to the Court of Session and they have found in our favour and and the council are still not paying us.
“They know we are due the money but it is really dragging on.”
Unions said members regret the action but hope people understand they have waited a long time for equality.
Unison regional organiser Mandy McDowall said: “This strike comes at the end of ten years of litigation through the courts.
“Last year the courts agreed with us that the council’s pay scheme was unequal and invalid and we were sent back to negotiate a new pay scheme and settlement of equal pay claims for thousands of women across Glasgow.
“In ten months and 21 meetings of negotiations we have got nowhere.
“There is no detail on the table that allows us to have confidence that the council will meet the deadline of December that was equally set.”
The local authority said it had explored all options to avert the strike.
Glasgow City Council leader Susan Aitken told BBC Radio Scotland: “The strike will have a devastating impact and there’s no need for it.
“They won their case the day that the SNP was elected to lead Glasgow City Council and we have been working ever since then to deliver them justice.
“We are extremely close to it and I am confident that they will get the settlement that they are entitled to and we will start paying out in the next financial year.”
First Minister Nicola Sturgeon retweeted a tweet from Scottish Labour Richard Leonard in which he said he sent “solidarity to the thousands of Glasgow women who are striking in their fight for justice.”
She added: “While I wish the strike wasn’t happening, I have nothing but admiration for the women involved.
“However, I feel contempt for a Labour Party expressing solidarity now when, in power, they took these women to court to deny equal pay. @theSNP and @SusaninLangside are working to fix.”
The local authority introduced its Workforce Pay and Benefits Review (WPBR) and grading scheme in 2006 to tackle inequalities.
Some female workers say the way it is structured led to people in female-dominated roles are being paid up to £3 an hour less than people in male-dominated roles.
Some women are said to have been paid up to £4,000 a year less than male counterparts.