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