Moving a project forward, even without managerial authority

Managing a project even though you don't have any hierarchical power: Mission impossible? Certainly, it is a difficulty which often only personal influence can overcome. It's a question of how to create authority.
Remember
Stop asking
It is tempting, when a project is not moving forward, to chase after contributors, to ask them for new due dates... which may work, in time, but at what price? After a few "regular" reminders, if nothing is really moving forward, then stop. Observe the situation and decide to act differently.       
Get them to take a position
What is the position of each of your contributors in the project? Is it in the interest of each of them to participate? What do they expect to contribute? What are their principal obstacles? Are there paths of action? … It's not your job to tell them "we have to" but also up to them and/or their supervisors to say "we will".       
Go or no-go
If the contributors embrace the idea of playing their part in the project, then it becomes necessary to remove the obstacles that prevent them from involving themselves as they would wish (organization, priorities, form and timing of deliverables...) If they do not embrace the idea, which may be for perfectly legitimate reasons, then it is preferable to envision replacing them, even if that creates even more difficulties initially.       
Evaluation

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