Type 31 of human adenovirus species A (HAdV-A31) is a significant pathogen primarily associated with diarrhoea in children but also with life-threatening disseminated disease in allogeneic haematopoietic stem cell transplant (HSCT) recipients. Nosocomial outbreaks of HAdV-A31 have been frequently described. However, the evolution of HAdV-A31 has not been studied in detail. The evolution of other HAdV types is driven either by intertypic recombination, where different types exchange genome regions, or by immune escape selection of neutralisation determinants. Complete genomic HAdV-A31 sequences from sixty diagnostic specimens of the past 18 years (2003-21) were generated, including fourteen specimens of a presumed outbreak on two HSCT wards. Additionally, twenty-three complete genomes from GenBank were added to our phylogenetic analysis as well as in silico generated and previously published restriction fragment polymorphism (RFLP) data. Phylogenetic analysis of eighty-three genomes indicated that HAdV-A31 evolved slowly with six lineages co-circulating. The two major lineages were lineage 1, which included the prototype from 1962 and nine recent isolates, and lineage 2, which split into four sublineages and included most isolates from 2003 to 2021. The average nucleotide identity within lineages was high (99.8 per cent) and identity between lineages was 98.7 and 99.2 per cent. RFLP data allowed the construction of a lower-resolution phylogeny with two additional putative lineages. Surprisingly, regions of higher diversity separating lineages were found in gene regions coding for non-structural and minor capsid proteins. Intertypic recombinations were not observed, but the phylogeny of lineage 3 was compatible with an interlineage recombination event in the fibre gene. Applying the phylogenetic analysis to the presumed nosocomial outbreak excluded two suspected transmission events and separated it into two different, simultaneous outbreaks caused by different sublineages of lineage 2. However, due to the high nucleotide identity within HAdV-A31 lineages, the proof of infection chains remains debatable. This in-depth study on the molecular phylogeny of HAdV-A31 highlights the high genetic stability of co-circulating HAdV-A31 lineages over almost six decades. It also supports the epidemiological hypothesis that HAdV-A31 circulates as an etiological agent of a childhood disease infecting immunologically naive patients without strong positive selection of immune escape variants and recombinants.