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Yes. There are FHA, VA and USDA insured or direct mortgages that do not require a down payment or do require a down payment but at a lower amount.
Also, there are down payment assistance programs (usually for low-income buyers and first-time homebuyers) that don't have to be paid back or are paid back only when the buyer moves out or sells the home. A HUD approved Housing Counselor can help find down payment assistance programs that are right for you. Find your local Housing Counseling Agencies here: HUD approved Housing Counselors by State