Culture presents a second inheritance system by which innovations can be transmitted between generations and among individuals. Some vocal behaviours present compelling examples of cultural evolution. Where modifications accumulate over time, such a process can become cumulative cultural evolution. The existence of cumulative cultural evolution in non-human animals is controversial. When physical products of such a process do not exist, modifications may not be clearly visible over time. Here, we investigate whether the constantly evolving songs of humpback whales ( ) are indicative of cumulative cultural evolution. Using nine years of song data recorded from the New Caledonian humpback whale population, we quantified song evolution and complexity, and formally evaluated this process in light of criteria for cumulative cultural evolution. Song accumulates changes shown by an increase in complexity, but this process is punctuated by rapid loss of song material. While such changes tentatively satisfy the core criteria for cumulative cultural evolution, this claim hinges on the assumption that novel songs are preferred by females. While parsimonious, until such time as studies can link fitness benefits (reproductive success) to individual singers, any claims that humpback whale song evolution represents a form of cumulative cultural evolution may remain open to interpretation. This article is part of a discussion meeting issue 'The emergence of collective knowledge and cumulative culture in animals, humans and machines'.