What is meant by near-critical path?

The near critical paths of a project may have small amounts of float -"little float"- as such, they must be completed in a timely manner or the overall project plan may be impacted in the same manner as by a critical path.

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the critical path is the path with zero float , the near critical path is the path with a small amount of float such that if any delays happen it may become critical

Agree with Mr Mohammed Helal 

thanks for invition ,,,,,,,,,, i agree with experts answers