* Dollar adds to Monday's gains
* Yen edges up but erases some of earlier gains s
* Currency volatility up but far from equity levels
* Graphic: World FX rates in 2018 http://tmsnrt.rs/2egbfVh
LONDON, Feb 6 (Reuters) - Currency markets showed far less of the panic movements gripping equities on Tuesday, with the dollar gaining slightly and traditional safe haven currencies like the Swiss Franc and the Japanese yen struggling to hold on to earlier gains.
The sell-off across world stock markets sent investors rushing into the dollar on Monday, helping the U.S. currency bounce amid a period of prolonged weakness against the euro, British pound and commodity-linked currencies.
But in early European trading on Tuesday the moves were less pronounced.
The dollar rose slightly, including against the euro, with the single currency 0.1 percent lower at $1.2358, down from the daily high of $1.2435.
The yen, which tends to attract investors at times of market stress, rose but gains were muted. The Japanese currency was up just 0.2 percent against the dollar by 1157 GMT,, having earlier climbed as much as 0.7 percent to hit a one-week high.
The Swiss franc lost 0.4 percent versus the euro to trade at 1.1577 francs,
"There's been quite a decoupling between equity market volatility and FX volatility. It may be that it's because of a breakdown in the dollar and Treasury yields," Valentin Marinov, London-based head of G10 FX Research at Credit Agricole, said.
Marinov was referring to the dollar's persistent weakness in the face of rising U.S. government bond yields, which usually push up the U.S. currency.
On Tuesday, the 10-year Treasury yield slid about 10 basis points to 2.696 percent, down from a four-year high of 2.885 percent set on Monday.
Analysts said that the dollar was unlikely to end its long period of weakness without a change in fortunes for the global economy, which is growing at a healthy rate and has so far showed no signs of slowing. That has boosted the euro to three-year highs and also helped sterling recover.
"We are seeing some of the classic signs in currency markets, with the yen...moving higher. But it's nothing dramatic," said Alvin Tan, London-based FX strategist at Societe Generale.
Currencies at risk of weakness amid the global equity slump are the higher-yielding commodity-linked currencies like the Australian dollar, New Zealand dollar and emerging market currencies, that tend to sell-off when risk appetite drops, analysts said.
Tan said if the sell-off in risk assets continued, he expected the dollar to gain further against the Australian and Canadian dollars, but to struggle against the euro and yen.
The Australian dollar weakened 0.4 percent to $0.7850 .
Sterling fell 0.4 percent and touched the day's low of $1.39.
For Reuters Live Markets blog on European and UK stock markets see reuters://realtime/verb=Open/url=http://emea1.apps.cp.extranet.thomsonreuters.bi z / c m s / ? p a g e I d = l i v e m a r k e t s (additional reporting by Shinichi Saoshiro in TOKYO; editing by William Maclean and Alexander Smith)