* FTSEurofirst 300 up 0.04 pct, Euro STOXX 50 flat
* Madrid, Milan, Lisbon, Athens, Dublin bourses extend rally
* Massive trading volumes in periphery
* Euro zone banks up 6.4 pct so far in 2014
PARIS, Jan 8 (Reuters) - European stocks paused on Wednesday around 5-1/2 year highs, but peripheral euro zone markets extended their rally on rising confidence that their economies are starting to recover from the regional debt crisis.
Trading volumes on Portugal's PSI 20 benchmark share index were nearly seven times the daily average, while turnover in Madrid, Milan and Dublin were at least 40 percent higher than average, according to Thomson Reuters data.
Peripheral euro zone stocks have seen hefty inflows recently and strong demand for an Irish debt sale, which has pushed down euro zone government bond yields, has raised expectations that Portugal will be able to exit its EU/IMF baiilout programme this year as planned.
At 1530 GMT, Spain's IBEX was up 0.8 percent, the PSI 20 was 1.3 percent higher, and Greece's ATG index had gained 3.3 percent.
The broad FTSEurofirst 300 index of top European shares was up 0.04 percent at 1,320.36 points, just shy of a 5-1/2 year high hit earlier in the session.
The euro zone's blue-chip Euro STOXX 50 index was flat, while the UK's FTSE 100 index was down 0.4 percent, and both Germany's DAX index and France's CAC 40 were off 0.1 percent.
"Overall, things are improving in the euro zone. Spain's recovery is gaining traction as all the efforts the country has made are starting to pay off," said Claudia Panseri, head of equity strategy at Societe Generale Private Banking, which has 84 billion euros ($114 billion) of assets under management.
"We're particularly positive on the shares of euro zone banks that already meet Basel III capital ratios. They have already significantly reduced their leverage and strengthened their balance sheets," she said.
The STOXX euro zone bank index was up 1.9 percent, extending its gains so far this year to 6.4 percent, about a quarter of its gains for the whole of 2013.
Spain's Banco Popular jumped 6.9 percent, Italy's Intesa Sanpaolo rose 2.5 percent and Portugal's Millennium BCP gained 2.9 percent.
Investors, pleased by recent signs of economic improvement in peripheral euro zone countries as well as by brisk demand seen on Tuesday at Ireland's first bond sale since it exited its EU/IMF bailout, have been pouring into the countries' bonds and stocks.
Spanish 10-year bond yields hit new four-year lows of 3.78 percent on Wednesday.
"It's all about the peripheral yields falling, that's what triggered the rally in equities. Investments are flowing in, which also explains why the euro remains so strong," said David Thebault, head of quantitative sales trading, at Global Equities.
"This is all based on the anticipation of an economic recovery, but it will take a good six months to see if there's a turnaround in the real economy. We're not there yet."
Today's European research round-up
Asset returns in 2013: