First of all, some stakeholder analysis has to be done. in case of negative stakeholders, it is important to understand what it is their influence on the project. I have found this analysis in "The Lazy Project Manager" by Peter Taylor. I believe it is a very simple, yet effective way to put things. So, for a stakeholder considering:
- Power on the project or in the organization
- Interest in the Project
So, typically, a negative stakeholder with a lot of interest and a lot of power must be handled very carefully. For this kind of stakeholders, things like involving them in the product design or asking for feedback on a very early phase of the project might be used. However the most important step is understand why they are negative stakeholders, i.e. what do they have specifically against the project.
For other stakeholders, the one with not so much interest in the Project but considerable Power or -the other way around- lot of interest but not much Power, a good communication management is usually sufficient. For instance, let us send them a report on the project -say- once every two weeks, or, even better, let's take the time to meet them personally and do a short report personally. Sometimes much better than a dry E-mail in those cases.
The other negative stakeholders, with less power and less interest, can of course be ignored, saving our time for most important tasks.