CHICAGO (Reuters) - When iconic motorcycle maker Harley-Davidson Inc (>> Harley-Davidson Inc) warned on Tuesday that discounting from foreign rivals would dent its profits, the message resonated beyond the motorcycle business.

From cars to construction equipment, the impact of the strong dollar is a big problem for U.S. companies selling overseas. But the U.S. dollar's recent surge to multiyear highs against major currencies, such as the euro and yen, has also become a challenge to their efforts to protect market share on home turf.

Harley's U.S. market share slipped nearly five percentage points in the first quarter to 51.3 percent as competitors offered discounts of up to $3,000 per bike and slashed suggested retail prices by up to 25 percent.

Honda Motor Co Ltd (>> Honda Motor Co Ltd) and Suzuki Motor Corp (>> Suzuki Motor Corp) both currently offer $1,000 (669.23 pound) cash back on selected models. Suzuki has cut the suggested retail price on 13 models and Honda is offering low-interest financing.

Harley says it will not compete on price to protect its brand, a declaration welcomed by industry analysts.

"They (Harley) are taking a reasonable long-term view of the market," said Michael Millman, founder of Millman Research Associates in New Jersey. "They want to maintain their pricing and their image and will have to take some of the competitive knocks that go with that."

AUTOS, HEAVY EQUIPMENT HIT

Harley-Davidson is not alone in feeling pricing pressures from the dollar. Many companies including Caterpillar Inc (>> Caterpillar Inc.) and U.S. automakers Ford Motor Co (>> Ford Motor Company), General Motors Co (>> General Motors Company) and Chrysler  (>> Fiat Chrysler Automobiles NV) also face tougher competition as result.

Unlike Harley, Caterpillar benefits from the natural hedge of having much of its production overseas, said Longbow Research analyst Eli Lustgarten.

The Peoria, Illinois-based construction equipment maker does face "stiff face-to-face competition" from Japanese rival Komatsu Ltd (>> Komatsu Ltd) when bidding on projects, he said.

Other market factors face Caterpillar besides the dollar. While the U.S. construction market is solid, Caterpillar's energy- and commodity-related businesses have "gone off the cliff" as oil and commodity prices have fallen, Lustgarten said.

But U.S. automakers face a different challenge. Many "foreign" brand vehicles are now built in the United States of parts sourced from North American factories, said Barclays analyst Brian Johnson.

Rather than competing on car price tags, automakers like Toyota Motor Corp  (>> Toyota Motor Corp) are instead likely to focus on adding more frills and gadgets to vehicles without raising prices.

This could put pressure on suppliers like Delphi Automotive (>> Delphi Automotive PLC) that produce added options like advanced driver assistance programs or infotainment, rather than GM, Ford or Chrysler directly, Johnson said.

To ride out the currency turmoil, manufacturers such as Harley, with production mostly in the United States, will have to weigh tough choices between cutting prices to spur demand, or cutting production to avoid getting stuck with too much inventory.

Jaime Katz, an analyst at Morningstar, said thanks to more flexible just-in-time manufacturing, Harley can quickly adjust production up or down. The company signalled it expects shipments to drop as much as 10 percent in the second quarter.

If the dollar remains strong, she will be watching to see if the motorcycle maker cuts its shipment forecast when it next reports earnings in July, as it did on Tuesday.

At some point, Harley could face a tough choice about what to do with its existing floor models if it cannot sell them later in the year, she added, noting that is some way off.

The problem with discounts is that customers come to expect them, said S&P Capital IQ equity analyst Efraim Levy.

"If you cut prices, people expect discounts hold out for a better deal," he said.

Foreign motorcycle makers are also taking a gamble by cutting retail prices that could hurt them if the dollar weakens, Levy added.

"Reinstating prices is harder than raising prices again," he said. "Then you run the risk of consumers getting sticker shock."

(Reporting by Nick Carey, additional reporting by Ben Klayman; editing by G Crosse and Joseph White)

By Nick Carey