Both Sheffield Green Party and the Liberal Democrats say there has been a lack of transparency and openness at Sheffield Council about who, and how, decisions are being made.
Green Party councillor Douglas Johnson and Liberal Democrat Leader Shaffaq Mohammed are both concerned about decision making powers being handed over to officers.
Council Leader Julie Dore has used emergency powers to allow officers to make decisions - something she can invoke without Cabinet or full council needing to approve it.
Coun Johnson said: "We have a strong leader model but she has handed a lot of power to officers.
"We should be able to see who makes all the decisions. Coun Julie Dore announced months ago that she was stepping down as Leader and stepping down as councillor and she should have done that.
"There is an awful lot of irony here that she didn't want to be Leader anymore but still is and has given officers power.
"It is really hard to know what decisions are being made and who is accountable. Cabinet members have been squeezed out and we have heard very little from either them or the Leader directly.
"We did not vote for officers, decisions should be made through the democratic process. There has been a complete abdication of any governance of the city."
Coun Shaffaq Mohammed said other councils and their leaders had been more transparent.
"Julie Dore has abdicated all responsibility for the city's leadership and we have officers making decisions who have not been elected through the ballot box.
"The Leader and Cabinet members get extra money with a special responsibility allowance but they are missing in action.
"We absolutely need political leadership but it has been completely lacking. Serious times need serious leadership."
Neither Coun Dore nor Sheffield Council were available for comment.