Successor Start Date same as Predecessor Finish date

Check the project start hour against your calendars.

Rafael gives good advice and the first thing to do when implementing it is to go to Edit > User Preferences... and set P6 to show the Time on the Dates tab.  I prefer 24 Hour format, just make sure it is not on Do not show time.

Then you can look at the Data Date on the Project and verify it has a sensible time.  The Time should be before the starting time of your Calendar, but to be safe it is best to set it to 00:00.

You will need to Schedule your project if you had to change it.  Now you can see the Time element in the dates as well.

I hope that helps.

Barrie

"Check the project start hour against your calendars."

Thanks Rafael, Barrie. My User Preferences is selected for "Do not Use Time" because I dont want to display time in my Dates columns.

But to try out your suggestion, I selected "24 Hour" and changed the start date/time from 20 Jan 2016 02 to 20 Jan 2016 00. This caused my ODs to change !! and the original problem (Finish Date of Activity A=Start Date of Activity B) remains.

It doe snot matter if you want to use times or not the program uses time regardless if you want to or not.

the problem is the TIME if you turn on your times you will see the issue.

also show your durations in decimals 

both of these items can be turned on by going to edit users preference 

the show time setting is in the Dates tab click 12 hour and show minutes

and the duration decimal setting is in the units tab under duration format make it 2 decimals 

in your situation a 1 day activity is starting on the 2nd half on the first day at maybe 12:00 noon. So 4 hours are worked on 2nd half of the 1st day. Then the remaining 4 hours are started on the begriming of the 2nd day say 8:00 am.

This means the successor can start on the same day as the predecessor finished which would start on the second half of the day.

to fix this 

Make sure that all your remaining durations are in whole numbers  

when you schedule F9 your project make sure that the data date TIME is set to 8:00 am or the earliest hours that is being used by your calendars.

going forward for all actual start dates make sure that the TIME is 8:00 am or the earliest hours that is being used by your calendars.

make sure that any actual finish dates have the TIME of 5:00 pm or the latest hour begin used by your calendars. 

make sure all start constraints that the TIME is 8:00 am or the earliest hours that is being used by your calendars.

make sure all finish constraints that the TIME is set to 5:00 pm or the latest hour being used in your calendars. 

Thanks Zoltan. That worked.

glad I could help