The present invention provides for the use of iota- and/or kappa-carrageenanfor the manufacture of an antiviralpharmaceutical composition for the prophylaxis or treatment of a pathologicalcondition or disease caused by or associated with aninfection by a respiratory virus selected from the group consisting oforthomyxovirus, paramyxovirus, adenovirus and coronavirus.The present invention further provides for the use of fucoidan, in particularof high molecular weight fucoidan, for the manufactureof an antiviral pharmaceutical composition for the prophylaxis or treatment ofa pathological condition or disease caused by orassociated with an infection by a respiratory virus selected from the groupconsisting of orthomyxovirus and paramyxovirus.