Polymeric nanofibers have been developed which are useful in a variety of medical and other applications, such as filtration devices, medical prosthesis, scaffolds for tissue engineering, wound dressings, controlled drug delivery systems, cosmetic skin masks, and protective clothing. These can be formed of any of a variety of different polymers, either non-degradable or degradable. In a preferred embodiment demonstrated in the following examples, nanofibers are formed of biodegradable and non biodegradable polyphosphazenes, their blends with other polyphosphazenes or with organic, inorganic/organometallic polymers as well as composite nanofibers of polyphosphazenes with nanosized particles such as hydroxyapatites.