CHICAGO, April 20 (Reuters) - U.S. corn futures climbed to their highest in nearly eight years on Tuesday and soybean futures neared a seven-year high as tightening supplies supported cash markets and attracted speculative buying, analysts said.

Worries about dry conditions curbing corn yields in Brazil and cold weather slowing germination of the 2021 U.S. crop added support.

Wheat futures followed the firm trend as freezing temperatures in the U.S. Plains and Midwest this week threatened developing winter wheat crops.

Chicago Board of Trade May corn settled up 14-1/2 cents at $6.06-1/2 per bushel after reaching $6.11-3/4, the highest price on a continuous chart of the most-active contract since June 2013.

CBOT July soybeans ended up 21-1/4 cents at $14.57-3/4 a bushel after rising to $14.71-1/2, the highest for a most-active soybean contract since June 2014. CBOT July wheat finished up 7-1/2 cents at $6.61-1/4 a bushel.

Life-of-contract highs were set in corn, soybean and wheat, as well as several soybean oil contracts.

Nearby futures posted the biggest advances in corn and soy, gaining against back months on signs of dwindling U.S. stockpiles.

"That is certainly showing up in the cash markets, with the basis that continues to ratchet higher as a sign of tightening supply. You see it in the spreads today," said Terry Linn, analyst with Linn & Associates.

Speculative buying by commodity funds was likely a factor as well, Linn said, noting that the CME Group, operator of the CBOT, expanded position limits in grain futures last month.

"The funds have deeper pockets than they did before," Linn said.

Tensions in related vegetable oil and biodiesel markets added to strength in soybeans. Traders have sold two shipments of Ukrainian rapeseed this month to Canadian buyers, a highly unusual trade, market sources said.

Brazil suspended import duties on soy, corn, soybean meal and soybean oil until the end of the year, the Agriculture Ministry said on Monday, as the country seeks to slow inflation.

(Additional reporting by Gus Trompiz in Paris and Naveen Thukral in Singapore; editing by Subhranshu Sahu, David Evans and Dan Grebler)