How is it possible for a time limit for my opponents move can be different  on his page from  the  limit given  on my page? In a recent game the limit for his move was given as 63 minutes on mine and three minutes on his. Five minutes later the reading was 58 minutes on my page and..wait for it.....'a few more minures'  on his. I do not understand this.

If they are on vacation, the time may be different......

If someeone is on vacation (he was not in this case) then both clocks stop, don't they? I still do not understand how this can happen.

I've also noticed some discrepancies in the remaining times displayed on different pages. I've never thought much of it - it might have something to do with the caching of webpages - since my opponent's time has always run out eventually, usually in accordance with the lowest time remaining.

your clock always stops when it's your opponent's turn (vacation time or no).

i have noticed a difference before as well. if it was vacation time, one clock could read very different from the other.