I am working in finance and almost everything is in excel. I love using links and formulas for getting data from different files. But this creates problem also like now a days I am getting following error massage..

"Excel cannot complete the task with the available resources. Chose less data or close other applications."

After clicking OK

Another massage comes is

"Unable to save external link values."

But if I close the file and do the same as above and reopen that file it appears as saved till the last when closed down.

Now I can't make out that if there is any problem in this or some problem is going to come.

You can overtake the plumbing with multiple external references. Although you are calling only a few cells, the system has to load the ENTIRE document into "background memory." So if the reference doc is HUGE, and you've referenced back and forth and across (the referenced doc has referenced docs and so on... ) then the amount of memory used shoots up exponentially.

I know this may sound scary, but you need to reorder your external references. You need to have two types of docs...
Docs with data and no references to other docs. Try to keep these docs reasonable in size, but you can have as many as you need.
Docs that reference other docs. Keep the number of these documents low, but the docs can be as big as you want.
Also, at this point I would make sure the computer you are working on has the MAX installed memory/speed available to the model.