Dunér was one of the founders of Astronomische Gesellschaft in Heidelberg 1863, and participated also in two arctic expeditions to Spitzbergen in 1861 and 1864, the later under the famous Swedish explorer Adolf Erik Nordenskiöld, performing determinations of fundamental value for the future maps of the islands.
At the observatory in Lund, he started working with spectroscopy in the late 1870's. He had earlier worked in the field of classical astronomy, celestial mechanics and double stars; 1867 - 1875 he carried out micrometrical observations of 445 double or multiple stars for calculating the motions of the components.
Dunér began a survey of the spectra of red stars (class III in Vogel's classification system), partly because of the idea that red stars were at a more advanced evolutionary level. Dunér produced a catalogue of the spectra of red stars, published in 1884. He also discovered more than one hundred stars of this type.
After his study of red stars, Dunér was appointed professor at the Uppsala observatory and started work on the solar spectrum using the new double refractor. He aimed at measuring the rotation rate of the Sun by measuring the Doppler shifts of the solar lines. Dunér measured the displacement of iron lines in the solar spectrum in relation to stationary lines produced by oxygen in the Earth's atmosphere. The careful measurements produced a view of the Sun's rotation at different latitudes, faster near the equator, with an accuracy not obtained by earlier observers.
Dunér became an astrophotographical pioneer in Sweden and published many articles on photographical techniques, the chemistry of developers etc in various journals.
He participated in the congress in Paris 1887 where Carte du Ciel was planned.
A text-book in Swedish; Handbok i allmän astronomi was also also published by Dunér in 1899.