Some Mannich bases of 7-hydroxycoumarin (2) and their simple derivatives (3 and 4) were prepared and tested against viruses containing single-stranded, positive-sense RNA genomes (ssRNA(+)). This study was directed toward Flaviviridae and, in particular, HCV surrogate viruses (BVDV, YFV). The 7-hydroxy derivatives 2 were generally devoid of activity, but when position 7 was propylated, the resulting 7-propyloxy derivatives 3 were in some cases endowed with an interesting activity against BVDV. The formation of 7-benzoyl derivatives 4 gave compounds generally lacking in activity against Flaviviridae, whereas the appearance of activity against RSV has been observed. Also some unsymmetrical methylene derivatives 5-7 (namely coumarins bridged to chromones or indoles) were found moderately active in antiviral tests. Derivatives 3 were submitted to a molecular modeling study using DNA polymerase of HCV as a target. The good correlation between calculated molecular modeling IC(50) and experimental EC(50) indicates that DNA polymerase is potentially involved in the inhibition of surrogate HCV viruses.