Germany's blue-chip DAX index pierced 5,000 points for the first time this month, to close 61.53 points, or 1.24 per cent, higher at 5040.15. Traders said the market had more upside despite the low volume before the euro launch on January 1st.
A trader from a German bank in Munich said volumes had reached their lowest point so far, but were expected to go even lower in the last two trading days of the year.
He also said that the market had reached a "very healthy level" and "definitely" expected the Xetra DAX to close above the 5,100 level on Wednesday.
French stocks closed flat at the end of a quiet, range-bound session, as thoughts turn to the euro changeover this coming weekend. The CAC-40 closed up 0.68 points at 3,873.10.
A Paris dealer said "nobody wants to make any big moves", adding: "A lot of people are still on holiday and others are testing their systems for the euro next week."
The lack of liquidity meant that individual orders created sharp price movements, "but the truth is there's nothing going on and no real news. Nobody is really watching Wall Street too closely, or the dollar, or any of the usual indicators. We're just biding our time until next week."
The Italian bourse ended almost three 3 per cent up after an unexpectedly lively pre-New Year session which saw merchant bank Mediobanca suspended limit up.
The Mibtel all-share index closed 2.84 per cent up at 23,720.
Telecom Italia closed up 477 lire at 14,475 after reaching a preliminary deal to sell up to 80 per cent of its loss-making pay-television unit, Stream, to Rupert Murdoch's New Corp.
