The Brazilian-Argentine Agency for Accounting and Control of Nuclear Material (ABACC) is a bilateral organization created in 1991 by Argentina and Brazil to verify the peaceful use of nuclear materials and installations in both countries. Among several responsibilities, ABACC has to perform quantitative verification of the declared nuclear material inventories and transactions by independent measurements, performed with systems and techniques that must conform to accepted international standards. In this regard, destructive assay (DA) techniques are of the utmost importance, mainly due to the high-performance levels they can meet in terms of precision and accuracy. ABACC uses DA techniques to detect small biases in the declared nuclear material quantities and to evaluate some of the measurement systems used by facility operators for establishing those declarations. In this paper we describe how ABACC implements DA in support to its mission: techniques being used, analytical laboratories involved and typical performance levels. We also evaluate the consistence between the values obtained by ABACC and the International Atomic Energy Agency (IAEA) as result of independent collection of samples during joint inspections performed in Argentina and Brazil over the last years. Finally, an update on the status of the ABACC-Cristallini UF6 sampling method in lieu of the conventional method is presented.