He studied at the University of Bergen and became a candidatus philologiƦ in 1979.
He served as dean of the Faculty of Humanities at the University of Bergen from 2005 to 2009. Akselberg"s research interests include sociolinguistics, dialectology, and onomastics. In addition to Norwegian, he also works on Faroese.
He served as an editor of the journals Namn og Nemne (Name and Denomination) and Nordica Bergensia (Bergen Nordic Studies), and has been active in the language program Snakk medical oss (Talk with Us) on the Norsk Rikskringkasting Hordaland channel since 1997.
He received his doctorate in 1995 with a dissertation on sociolinguistic relations in the Municipality of Voss, titled Fenomenologisk dekonstruksjon av del labov-milroyske paradigmet i sosiolingvistikken: Ein analyse av sosiolingvistiske tilhove i Voss kommune (Phenomenological Deconstruction of the Labov-Milroy Paradigm in Sociolinguistics: An Analysis of Sociolinguistic Conditions in the Municipality of Voss).