Humidity is the most likely candidate. Specifically if you are running air conditioning. Hot moist air comes into contact with a cold surface, such as concrete and condenses on that surface.
Are your ducts insulated? If not that is a possible solution and now a code requirement to meet energy efficiency guidelines.
Heat travels from warmer to cooler. Depending on if the condensation is on the outside or inside of the ducting would help determine the cause. I have seen condensation issues many times in the winter from homeowners using other forms of heat that create a warm moist environment, like a fire place, while not running the central heating. This causes the duct work to dry out the duct, thereby causing condensation to form on the inside of the ducts when the warm moist air transfers from inside the ducts to the cooler environment surrounding the outside of the ducts.
While all of the above is true - you could try to run a dehumidifier in the basement and see if it helps to reduce condensation on the ductwork.
Or have a professional to install additional returns/supplies in the basement if possible.