* Portugal's BES takes steps to ease worries over its health
* Portuguese yields fall, periphery markets stabilise
* Last week's sell-off a reminder euro zone problems not fixed (Updates prices, adds fresh quotes)
By Marius Zaharia
LONDON, July 14 (Reuters) - Portuguese bond yields fell further on Monday after the country's biggest bank took steps to reassure investors over its stability, calming peripheral debt markets after their first episode of contagion this year.
Recent disclosures of financial irregularities at a web of family-held holding companies behind Portugal's largest listed bank, Banco Espirito Santo, had pummelled the country's stocks and bond markets.
BES said last week that it had 2.1 billion euros in capital above minimum regulatory requirements, which would cover any losses for its 1.15 billion exposure to Espirito Santo.
On Monday BES said its board has put in place new executives who were originally supposed to take over at the end of July, after the Bank of Portugal brought forward management changes there aiming at distancing the bank from the financial woes of its founding family.
The Espirito Santo family also sold part of its stake.
Portuguese 10-year bond yields fell 6 basis points to 3.83 percent, retreating further from a six-week high above 4 percent hit last week. Spanish, Italian and Greek bond yields were flat or a touch lower.
Last week, the sell-off in Portuguese bonds spread to the euro zone's other weaker members and hurt demand at Greece's second bond sale after its 2012 default in the first significant bout of debt market contagion in 2014.
"We've heard from BES that the risks can be contained," said Christian Lenk, a strategist at DZ Bank. "Markets are taking a step back, thinking about what happened last week and realising it's not the end of the world, it's not the end of Portugal.
"The memory of what happened during the crisis is still very fresh, like a trauma. That's why markets reacted this way... On the other hand to a certain degree it's justified. Yields have normalised, but there are still large long-term risks in the periphery."
Rabobank market economist Emile Cardon said last week's concerted sell-off of peripheral debt was a sign that investors remained nervous about the debt sustainability of these countries even as they bought the high-yielding bonds.
"There's still reason to believe that not all problems were resolved in the euro zone and we will continue to see bouts of volatility during a fragile recovery," he said.
Credit Agricole rate strategist Peter Chatwell said the fact that Portugal had already raised some of the funds it will need next year and that there was still a residual 6 billion euros from its rescue programme available for its banking sector should prevent an extended escalation of the periphery sell-off.
"But the risk is for the periphery to remain vulnerable in the near-term until there is more information on the situation and a plan of action," Chatwell said.
Elsewhere, Slovenian 10-year bond yields were 7 bps lower at 3.20 percent after political newcomer Miro Cerar led his party to victory in elections on Sunday.
Hiccups in Slovenia's privatisation programme lifted Slovenian bond yields in recent weeks, but some investors said they would use that as a buying opportunity, betting Cerar can reduce the government's 50 percent stake in the economy and cut the budget deficit. (Reporting by Marius Zaharia; Editing by Hugh Lawson/Nigel Stephenson)