* Spanish, Italian yields continue to fall
* Optimism on summit moves lingers
* But volatility reflects implementation worries
By Kirsten Donovan
LONDON, July 2 (Reuters) - Spanish and Italian government bond yields continued to fall on Monday after euro zone leaders last week surprised markets by agreeing measures to stabilise bond markets in an attempt to stem the debt crisis.
Under pressure from Spain and Italy, euro zone leaders agreed on Friday to let their rescue fund inject aid directly into stricken banks from next year and intervene on bond markets to support troubled members, moves that helped yields on the two countries' bonds ease.
But trading was volatile, particularly in core German Bunds, reflecting some hesitation with markets hungry for details of the measures and questions over how far the limited funds available in the region's rescue funds could be stretched.
The Finnish government said it would block the bailout fund from buying bonds in the secondary market, while the Netherlands said it did not support such action and would evaluate on a case-by-case basis.
"It's a pivotal moment, can Friday's decisions hold up and get implemented," said Credit Agricole rate strategist Peter Chatwell.
"If they can it's a net positive for the periphery but the risk is that a core nation like Finland attempts to derail the process by saying they don't want certain aspects of it."
Ten-year Spanish yields were down 3 basis points at 6.30 percent and two-year yields were down 16 bps at 4.24 percent. Both were off their best levels of the day but still leaving the yield curve around 60 basis points steeper since Thursday's close.
"The steepening is being led by the front end as default risk is priced out of the market so using this as a barometer of residual optimism from the summit, it suggests that the proposals do appear to have legs," Rabobank strategist Richard McGuire said.
Italian 10-year yields fell 8 basis points to 5.74 percent, while two-year yields dropped 19 basis points to 3.61 percent.
"We really haven't seen many flows this morning, either in the periphery or in core bonds," a trader said.
"You have to wait for details to be ironed out but for now we're just moving on headlines."
Spain and Italy's yields - or funding costs - remained high versus historical levels and a Spanish bond auction on Thursday will be the first test of market sentiment since the European Union summit last week, with the country expected to sell up to 2.5 billion euros of paper.
Trading volumes are likely to remain thin ahead of Thursday's European Central Bank policy meeting and Friday's U.S. employment data, which is often a big market mover.
The ECB is expected to cut its main refinancing rate 25 basis points to 0.75 percent on Thursday, with expectations that the deposit rate it pays banks to park cash overnight may also be cut to zero.
"A rate cut will be welcome, but while a short-term boost to sentiment, this is not a game changer," Societe Generale economists said in a note.
"With credit channels still impaired, a rate cut is unlikely to significantly improve funding conditions for banks or sovereigns in the periphery."
September Bund futures were 2 ticks lower at 140.88 in extremely choppy trading, with 10-year yields little changed at 1.585 percent.
"They delivered more than expected last week and markets did the right thing on Friday, although it was very quiet," said a second trader.
"But it wasn't a game changer, the periphery may stabilise heading into the ECB meeting but that's probably about the best you'll see."
Coupon and redemption payments from Germany totalling around 40 billion euros this week should help support core paper, along with the prospect of another 50 billion euros of cash inflows from France, Austria and the Netherlands next week.