I know that when debt is being re-paid, one pays interests along with repayment of some parts of debt principal. However, I am wondering a case where no part of debt principal is re-paid while interests are being paid. Is this possible in the U.S.?
The term you are looking for is "interest only loan". They certainly exist in the US, and for some cases are common. For example bridging loans are usually interest only.
They are generally used where there is a reasonable expectation that the borrower will be able to pay off the loan due to a change of circumstances sometime in the future - such as the bridging loan. However they are not favoured in most circumstances because lenders typically want to see evidence that the borrower will be able to pay off the loan when the time comes.
Here is a typical tutorial link: http://banking.about.com/od/mortgages/a/interestonlyln.htm
Interest only mortgages were popular several years ago; banks would lend on an interest-only basis for several years, on the assumption that rising house prices and improving wealth would allow the mortgagee to begin paying back the principal after a few years. In some cases the loan conditions went further than that, allowing interest to be added to the principal. Many consider that these practices contributed to the mortgage crisis of the last few years.
Interest only loans were also popular in the UK in the 80s and 90s, combined with an investment vehicle that would pay off the principal of the mortgage when they matured. These were called 'endowment mortgages'. They are no longer popular since the investment vehicles performed much worse than promised and typically did not pay enough money to cover the principal.
For mortgages in the United States, interest only loans exist, if this is what you're asking (the double negative confused me). While controversial, they can provide advantages to people willing to take the risk of principal-increase speculation (some investment houses offer similar products).
I've seen situations (as a banker) where customers would arrange to pay only interest on various loans, like auto, home equity, or personal loans for a period of time, usually because of a financial hardship. None of those loans, however, were arranged as interest-only, but were negotiated for a period of time, which (as you can read in the above link) many financial institutions do not offer.
Added: many people do what you're asking with lines of credit; pay only interest without payments to principal.