Problem with beveling edges

 From:  mdesign
8713.1 
I would like to bevel those edges. I`ve tried it without success. Surfaces are watertight. I`ve build it as "network" from curves. I want to smoothly blend those surfaces. I`ve thought about 10mm bevel. I think that I`m doing something wrong.



May you point me to right direction.

Thanks in advance.
Attachments: