Connecting two devices to one relay?

I have two device (each with his own separate dc transformer) that need to controlled by a relay, and i have only one relay.

Can i connect the both grounds to the same relay (the ground of the two will be touching each other)?

No.

Show us the devices, explain why and how you want them to be controlled.

Photos, please, perfectly focused and posted here as links to where they are lodged using the "image" icon (not using the "Attachments and other options" function which does not work properly). Or weblinks to the reference pages for the devices, and your relay.

Use a DPDT contact relay.