Anti-Gunrunning Act of 1999

Anti-Gunrunning Act of 1999 - Amends the Brady Handgun Violence Prevention Act to prohibit any licensed firearms dealer: (1) during any 30-day period, from selling two or more handguns to an unlicensed individual; or (2) from selling a handgun to an unlicensed individual who purchased a handgun during the 30-day period ending on the date of the sale. Provides that such prohibitions do not apply to an exchange of one handgun for another. Prohibits an unlicensed individual from purchasing two or more handguns during any 30-day period.

Provides for imprisonment for up to five years (currently, one year) for a licensed dealer, importer, manufacturer, or collector who knowingly makes any false statement in connection with required firearms records.

Extends the deadline for the destruction of records relating to handgun transfers subject to the waiting period from 20 business days to 35 calendar days after the date the transferee made the statement on the basis of which notice of the transaction was provided to the chief law enforcement officer of the place of residence of the transferee. Requires the national instant criminal background check system, if receipt of a firearm would not violate Federal or State law, to destroy records relating to the person or the transfer within 35 calendar days after the date the system provides the licensee with the identification number unique to the transfer.