When you import var into mod1 :
 from mod2 import var,fun_of_mod2 
You give it the name var in the mod1 namespace. It is as if you did this:
 import mod2 var = mod2.var fun_of_mod2 = mod2.fun_of_mod2 del mod2 
In other words, there are now two names for the value, mod1.var and mod2.var . They match at first, but when you reassign mod1.var , mod2.var still points to the same thing.
What you want to do is simply:
 import mod2 
Then select and assign the variable as mod2.var .
It is important to note that global variables in Python are not truly global. They are global only for the module in which they are declared. To access global variables inside another module, you use the module.variable syntax. The global operator can be used inside a function that allows you to assign a global-global name (without it, assigning a variable makes it a local variable in this function). This has no other effect.