Systematic investigations of the ultraviolet spectra of the hydrogen-rich white dwarfs were conducted with the International Ultraviolet Explorer satellite (IUE). This is to follow up on the work reported in Nelan and Wegner (1985) that the strong absorptions found earlier near lambda lambda 1600 and 1400 (cf. Greenstein 1980; Wegner 1982 and 1984, b) in the spectra of the cooler DA are absorptions produced by the H2 and H2(+) quasi-molecules. Observations of new DA white dwarfs obtained with the IUE are summarized.