Question
I have a leafy hedge that has groups of dead leaves - the stems are still green - some of the stems have both brown and green leaves - what to do?

Answer
I really need to know the plant name to make the best recommendation.  My inclination is to spray with a fungicide, since what you describe sounds like a fungal branch or twig dieback.  Do not cut off any branch that is green and has brown leaves, as it may come back out.  You can and should cut off all branches that are dead with brown leaves, as they will not come back out.  I would treat the hedge with Daconil fungicide which can be applied to almost any plant.  The fungicide should stop the dieback.  Re-treat the plant in 7-10 days then sit back and see how the new growth looks.  If you continue to see dieback increase, you may need to treat again. Good Luck.