The unions said members had been refused enhanced payments for their increased workload over the holidays. Leeds City Council said the unions' demands were "totally unreasonable" and the action would disrupt services. Staff working at household waste sort sites are also taking part in the action.
In a joint statement, the GMB and Unison said: "Our dispute is not with the people of Leeds but the city council that is supposed to serve them.
"This dispute is about our members being paid the appropriate rate for the vital service they provide and for being recognised where they work above and beyond the call of duty.
"If Leeds City Council will not do that then our members will work to their contracts, no more, no less. They will work to rule."