* Markets expect fewer hikes next year than Fed
* Credit rallies, Greek yields tumble
* Dollar strength seen taking pressure off ECB
* Spanish bonds lag ahead of weekend vote (Updates prices, adds quote)
By Marius Zaharia and John Geddie
LONDON, Dec 17 (Reuters) - Euro zone bond yields fell on Thursday, with investors encouraged by the Federal Reserve's commitment to gradual and data-dependent tightening of monetary policy after its first interest rate increase in nearly a decade.
Money markets and short-term bond yields showed no immediate reaction, suggesting investors do not see the Fed move altering the outlook for the European Central Bank, which should be pleased with the weaker euro.
The U.S. central bank made clear after the long-awaited rate move that its next step would depend on monitoring inflation, which remains below target.
Fed policymakers' median projected target interest rate for 2016 remained 1.375 percent, implying four quarter-point hikes next year.
Markets price in only two increases, reflecting bigger concerns about the economy and doubts about significant inflation. That helps explain why linking future moves to upcoming data gives investors more comfort that tightening will not be unwarranted.
German 10-year Bund yields were 6 basis points lower at 0.61 percent, while their U.S. counterparts fell 3 bps to 2.26 percent.
Most other euro zone bond yields were 3 to 6 basis points lower.
"There were fears of a mistake from the Fed if it were too confident or too hawkish," said Eric Vanraes, fixed income portfolio manager at EI Sturdza Investment Funds. "But it was good news ... so phew! We can go on the Christmas holiday. We can have a small rally everywhere."
Vanraes was more pessimistic than the Fed.
"I'm afraid they will raise maybe once or twice and there's a high probability that in Q3 or Q4 they might even have to decrease again the Fed funds rate," he said.
The iTraxx Europe index, which is derived from the credit default swaps of 125 investment-grade companies, was 3 bps tighter at 76 bps, reflecting increased risk appetite.
The iTraxx Crossover, based on the CDS of 75 of the most liquid sub-investment grade companies, was 10 bps tighter at 318 bps.
"Markets like certainty over uncertainty so when the Fed acts in a way that the market is expecting, it is not surprising that they react favourably," said Niklas Nordenfelt, portfolio manager at Wells Fargo Asset Management's US High Yield Bond Fund.
Greek 10-year bond yields, which often track emerging markets, fell 21 bps to 8.20 percent.
Euro zone money market rates implied a 40 to 50 percent chance the ECB will cut its deposit rate another 10 basis points next year, unchanged from before the Fed meeting. No immediate moves were foreseen.
Analysts said for now the ECB would be satisfied with the weaker euro, which fell 0.9 percent against the dollar, as well as with the lower bond yields.
Two weeks ago, the ECB lowered the rate it offers banks for overnight deposits to minus 0.30 percent and extended by six months, until March 2017, its programme of 60 billion euros a month in asset purchases.
The moves fell short of market expectations. But as oil prices collapsed to their lowest levels since the global financial crisis, inflation expectations resumed falling and bets for further monetary easing reappeared.
Similar worries are fuelling doubts about a fast-paced tightening in the United States.
"However smooth this first hike will be digested by markets, the real test for the Fed comes in 2016," said Stefan Kreuzkamp, CIO at Deutsche Asset & Wealth Management, who expects two more hikes next year.
"Amidst the somewhat lacklustre economic environment, investors will be left guessing at what FOMC meetings the next hike will be decided and when not."
Spain closed its 2015 debt programme with a lacklustre auction on Thursday, as investors with one eye on uncertain national elections this weekend demanded higher yields to buy the country's bonds.
The Treasury sold 2.1 billion euros, below its mid-range target of between 2 billion and 3 billion euros, just reaching its overall 2015 bond issuance target of 139 billion euros.
Sunday's election is tipped to result in one of Spain's most fragmented parliaments in decades.
Spanish 10-year yields fell the least in the euro zone, trading at 1.75 percent. (Reporting by Marius Zaharia and John Geddie, editing Jeremy Gaunt)