The National Audit Office say that there there have been "material errors" in the calculations of child maintenance assessments.
The watchdog's head Sir Amyas Morse qualified his audit opinions and said the figures did not give a "true and fair view" of the actual arrears.
The criticisms cover the schemes established in 1993 and 2003, which have subsequently been replaced by a separate system in 2012.
We really do need a system that works for both parents and that can be seen to be fair and efficient. If you are having problems with child maintenance issues please call the team on 0845 128 6960.
The NAO found that under the older schemes, the cumulative total of outstanding arrears since the Child Support Agency was established in 1993 stood at £3.957 billion. The money is owed by non-resident parents to the parent caring for the child or, in some cases, the secretary of state, and the arrears can only be written off in very limited circumstances.