"Use a comma to set off parenthetical elements, as in "The Founders Bridge, which spans the Connecticut River, is falling down."

Look at rule n° 4 in the link below. Good explanation.

Grammatically speaking, there always must be a comma before which. See why:

http://www.bartleby.com/64/C001/062.html#THAT

that / which (restrictive and nonrestrictive clauses). The standard rule requires that you use that only to introduce a restrictive (or defining) relative clause, which identifies the person or thing being talked about; in this use it should never be preceded by a comma. Thus, in the sentence The house that Jack built has been torn down, the clause that Jack built is a restrictive clause telling which specific house was torn down. Similarly, in I am looking for a book that is easy to read, the restrictive clause that is easy to read tells what kind of book is desired. 1
By contrast, you use which only with nonrestrictive (or nondefining) clauses, which give additional information about something that has already been identified in the context; in this use, which is always preceded by a comma. Thus you should say The students in Chemistry 101 have been complaining about the textbook, which (not that) is hard to follow. The clause which is hard to follow is nonrestrictive in that it does not indicate which text is being complained about; even if it were omitted, we would know that the phrase the textbook refers to the text in Chemistry 101. It should be easy to follow the rule in nonrestrictive clauses like this, since which here sounds more natural than that. 2
Some people extend the rule and insist that, just as that should be used only in restrictive clauses, which should be used only in nonrestrictive clauses. By this thinking, you should avoid using which in sentences such as I need a book which will tell me all about city gardening, where the restrictive clause which will tell me all about city gardening describes what sort of book is needed. But this use of which with restrictive clauses is very common, even in edited prose. If you fail to follow the rule in this point, you have plenty of company. Moreover, there are some situations in which which is preferable to that. Which can be especially useful where two or more relative clauses are joined by and or or: It is a philosophy in which ordinary people may find solace and which many have found reason to praise. You may also want to use which to introduce a restrictive clause when the preceding phrase contains a that: We want to assign only that book which will be most helpful.

Pia writes me that

>I have tried twice now to post my answer to your request, but I don't think it worked!

, which it didn't.

seems like this site is sometimes buggy as hell, which some of you probably already noticed, but, which i don't really pay any mind to.

so she asked me to post her clarification for her, which, here
goes:

[Original Sentence : ]

>"After regaining independence, Ukraine attempted to maintain a central
planned economy policy, which in late 1993 led to an economic crisis, which
nearly led to hyperinflation."

>What I need to know is: can/should both ','s be there or perhaps none of them and why.

the explication of the Rules given by Gayle, uFO and Sheena seem reasonable enough to me, but i just fly these things by the seat of my pants --like Duke Ellington said above, which sounds like a pretty good rule of thumb
for a lot of things in this life.

actually, i could see/hear this both ways, the first works, but so does this
one :

"After regaining independence, Ukraine attempted to maintain a central planned
economy policy which, in late 1993, led to an economic crisis which nearly led to hyperinflation."

[no preceeding comma, in either instance]

this seems better to me than :

"After regaining independence, Ukraine attempted to maintain a central planned
economy policy, which, in late 1993, led to an economic crisis, which nearly
led to hyperinflation."

on the theory that, in certain cases, "in late 1993" might warrant being set off by commas by itself for emphesis and, which would therefore leave that first "which" out there chopped up as its own little one-word clause, looking a bit too fussy and, which is *really* fussy when there's a comma before the second, which.

but, that's a special case.

, which is why i axed for the sentence in the first place, so that we could
try and figure out, which sounds best.

if you see what i'm saying.

iOw, depending upon, which part of the sentence you wish to emphasize, which can be preceeded by a comma or not, but, if it is, then you need to take care not to end up with a sentence, which looks overly fussy because you've preceeded each of your, witches by commas, which is an overly slavish subserviance to the Rules, which might put your reader off, depending upon, which language he or she speaks, if you can see what I'm saying.

Tricky question.