The invention provides systems, methods and kits for the separation and/or purification of double-stranded and single-stranded nucleic acids from the same sample. The method includes first mixing a sample containing both double-stranded nucleic acid and single-stranded nucleic acid with a solution including a chaotropic salt and a non-ionic detergent to generate a mixture; then applying the mixture to a first mineral support for double-stranded nucleic acid to bind; and collecting the flow-through which contains unbound single-stranded nucleic acid. The method further includes diluting the non-ionic detergent of the flow-through, and applying the diluted flow-through to a second mineral support for the single-stranded nucleic acid to bind. Alternatively the flow-through can be mixed with a lower aliphatic alcohol prior to loading of the second column. The double-stranded and the single-stranded nucleic acids can be eluted from the mineral supports respectively.