Stock markets around the world have been on a tear over the past few years. But now that the bull runs in the U.S. and in many emerging-market economies are beginning to look tired, investors may want to turn to the Old World.

Yes, Europe has had nice run as well. But the economy isn't as far along in the economic cycle as the U.S., and many European companies are still undervalued, relative to their U.S. counterparts. So the rally should still have some legs, say some fund managers.

"The European economy is accelerating as the U.S. economy slows," says Clas Olsson, co-lead manager of the $1.62 billion ( AEDEX) AIM European Growth Fund (AEDEX).

Olsson points out that the price-to-earnings ratio of the Stoxx 600, which represents 600 large-, mid- and small-cap companies across 18 European countires, is just 14, on the basis of earnings estimates for 2007. That compares with a P/E of 16 for the S&P 500.

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The fund manager says attractive valuations aren't the only things European companies have going for them, however. Many are involved in U.S.-style restructurings that are weeding out inefficiencies and making them more efficient.

What's more, the corporate tax rate is lower in Europe, having fallen dramatically over the past 10 years to 36% from 50%, according to Olssen. And the European consumer, who has a lot of cash but no confidence, has more buying power than the U.S. consumer, who has no cash but lots of confidence.

AIM European Growth has benefited from these trends, posting annualized returns of 19% over its 10-year existence.

It's up 12.7% for the year to date through June 30, and it has three-year annualized returns of 29.1% and five-year annualized returns of 23.5%.

By comparison, the average European fund tracked by Lipper is up 12.1% this year through June 30 and has an annualized three-year return of 25.4% and an annualized five-year return of 19.9%.

AIM European Growth has a front load of 5.5% and an expense ratio of 1.58%. It comprises 46% large-cap stocks, 32% mid-cap and 22% small-cap stocks.

The fund's strategy is actually a kind of blend of growth and value disciplines that Olsson and his team call "EQV," for earnings, quality and valuation. AIM defines quality as the company's return on equity and cash flow, while valuation corresponds with the stock's price-to-earnings ratio.

The focus is to identify "quality companies that have experienced or exhibit the potential for accelerating or above-average earnings growth, but whose valuations do not appear to fully reflect these attributes," Olsson says.

This helps the fund managers find high-quality growth companies that the market isn't focusing on. And by getting in the door early, the fund holds stocks for the long haul. That leads to low turnover: just 28%, according to Morningstar.

However, if a European fund is too concentrated for you and if you can only hold one international fund, Olsson also co-manages the ( AIIEX) AIM International Growth Fund (AIIEX). It's up 15.2% year to date and has returned an annualized 26.5% over the past three years and 18.6% over the past five years.

By comparison, its benchmark index, the MSCI EAFE, is up 10.4% so far this year and has returned an annualized 20.2% and 15.4% for the three- and five-year periods, respectively.

The International fund allocates about 60% of assets to Europe, 14% to Japan and 16% to the rest of Asia.

Both the European and the International fund hold Porsche, a German automaker with a strong brand that's leveraged into new products. "Other carmakers have very poor return on capital," Olsson says. "But these guys have pricing power and have doubled their volume in just six years."

Jason Holzer, the other co-manager on the European Growth Fund, also likes CRH ( CRH), an Irish company involved with the manufacturing and distribution of building materials such as cement, tiles and bricks.

"It's a terrific company with a successful track record of acquiring companies and folding them into their network," says Holzer. "It's selling at 13.5 times 2008 earnings and has a free cash flow yield between 7% and 8%."

Holzer also likes Anglo Irish Bank , which is a holding of both the European and International funds. Active in Ireland and the U.K., it's primarily a lender to small and medium-sized businesses.

"It's one of the most efficient banks in Europe," says Holzer. "And at 30%, it has the highest return on equity of any European bank. Despite its tremendous record, it sells at 10 times 2008 earnings, the same multiple of the average European bank."

Other American depositary receipts in the European fund's top 10 holdings include Petroleum Geo Services ( PGS) and Syngenta ( SYT).

The International fund holds UBS ( UBS), Teva Pharmaceuticals ( TEWA) and the WPP Group ( WPPGY).