UNTIL RELATIVELY RECENTLY, Big Oil gave little thought to sub-Saharan Africa beyond the coast of Nigeria and Angola. That's changing rapidly after a significant find off the Atlantic coast of Sierra Leone, where both Anadarko Petroleum (APC) and U.K.- based Tullow (TUWLY) have exploration licenses, and another strike in Uganda, where Tullow operates.

Their stocks have jumped sharply this year, mostly on the prospect of world-class fields. Tullow shares, up over 100%, have returned to 2008 highs set when crude was about twice today's $78 a barrel, but Anadarko, up 73%, remains below its 2008 high. So the questions are, how much oil is there, and is it reflected in the stock prices?

This prospect will be more definitively appraised as new wells are drilled over the next 12 months, but there is a persuasive case that the potential could top a billion barrels in West Africa. If that proves out, as bulls predict, then shares of Tullow and Anadarko remain undervalued, even after the run-up. Tullow's main trading is in London (TLW.UK), where the stock closed Friday at £12.36; Tullow's U.S.-traded shares, each equal to 10 U.K. shares, finished at 202. Anadarko closed around 67.

One of the wells generating the excitement, called Venus, hit more than 45 net feet of hydrocarbons off the coast of Sierra Leone, Anadarko said last month. It's 40%-owned by the U.S. company and 10% by Tullow. Few holes have been poked in the new West Africa prospect, so Venus' location is key, creating a possible bookend that -- with the large Jubilee field at the prospect's other end off the coast of Ghana, discovered in 2007 -- suggests the entire 1,100-kilometer coast could hold hydrocarbons. The other recent significant strike, made by Tullow, is in the Lake Albert area of Uganda.

It's difficult to estimate, but "Venus shows there is a working petroleum system and opens up the potential for more discoveries [along the Sierra Leone-Ghana coast] to be full of oil," notes Christopher Brown, the lead analyst for sub-Saharan Africa for Wood MacKenzie, an Edinburgh-based energy-and-resources consultancy. At minimum, the exploration licenses to drill in that region are more valuable than they were six months ago, he adds.

Wood MacKenzie doesn't comment on how much oil is in the entire prospect, but Anadarko and Tullow's analysis says the Jubilee field, in which they own 24% and 35% stakes, respectively, holds anywhere from 600 million to 1.8 billion barrels.

Earlier this month, that field received a big boost from ExxonMobil (XOM), which is reportedly battling China National Offshore Oil Corp., or Cnooc, to buy effectively a 23.5% stake held in Jubilee by Kosmos Energy at a price of $4 billion. The Jubilee field is expected to come online in the third quarter of 2010 and eventually produce 120,000 barrels a day.

"I don't know if you can get a better vote of confidence than that," says Oswald Clint, a London-based Sanford C. Bernstein analyst with an Outperform rating on both Tullow and Anadarko. Given Exxon's traditionally conservative approach, it suggests Jubilee is profitable at significantly less than the current oil price.

The bookended wells, says Sreejith Banerji, a Vontobel portfolio manager and former oil and gas engineer, mean "it's more than speculation [now]....There is a very high chance of a significant resource." Banerji still calls Tullow's stock cheap. "It's doubled, but off very depressed levels." Vontobel, which according to Bloomberg owns about 140,000 shares, hasn't sold into the rally.