Is it proper to connect Grounds from two different circuit which are individually powered from two different power sources ?

 

It depends on what exactly ground is (earth, common, etc...) and what ground does (safety, power, signal shield, etc...) for the different circuits.

 

IT can be done in most circumstances.
Do you have an example?
One method is called equi-potential bonding.

 

IT can be done in most circumstances.
Do you have an example?
One method is called equi-potential bonding.

Yeah I do have an example.

 

It depends on what exactly ground is (earth, common, etc...) and what ground does (safety, power, signal shield, etc...) for the different circuits.

Its a common ground in both circuit .

 

"Ground" is a rather nebulous term, and so is the answer, which is "Probably it is OK, but it depends..."
If it is that "ground terminal" on the back of pieces of a stereo music system, the certainly it is OK, but if it is the connector shield on portable mobile electronic items it may not be. That is because some manufacturers tie the supply positive to the frame, while most tie the negative to the frame.
If the "ground" connections are to parts tied to the third-pin (green wire ground) of the power connector, then certainly YES. \
And if all of the devices are powered by internal batteries, then Probably Yes, if the internal power is not tied to exposed conductive parts of the hardware.
So my suggestions are two: First, for battery powered devices, use a meter to check for any voltage between exposed metal on the different units after their "grounds" are connected. For mains powered devices, us the meter to check for voltages between exposed metal surfaces BEFORE connecting the "grounds."

And beware that in some instances, connecting frames to each other can lead to noise in the systems.

I discovered that with older an older battery powered VCR/Camera system that was intended to be powered by an internal 12 volt battery. The frame was tied to the positive battery terminal, which was OK until I tried to use an an adapter I made to replace the battery. The "hot frame in a negative ground car is asking for trouble.

 

Its a common ground in both circuit .

What is the nature of the 'Circuits' ?

 

To elaborate on what Max asked, What sort of devices are you asking about? Mains powered? Internal batteries powered?? Or 12 volts from a vehicle power jack powered, OR something else that I did not name? Are the devices otherwise connected to each other??
The fact is that if they should be commond with each other depends very much on what they are and what they are doing.

 

Yeah I do have an example.

OK. Please enlighten us with your example.