After demyelinating insult, the neuronal progenitors of the adult mouse sub-ventricular zone (SVZ) called neuroblasts convert into oligodendrocytes that participate to the remyelination process. We use this rare example of spontaneous fate conversion to identify the molecular mechanisms governing these processes. Using in vivo cell lineage and single cell RNA-sequencing, we demonstrate that SVZ neuroblasts fate conversion proceeds through formation of a non-proliferating transient cellular state co-expressing markers of both neuronal and oligodendrocyte identities. Transition between the two identities starts immediately after demyelination and occurs gradually, by a stepwise upregulation/downregulation of key TFs and chromatin modifiers. Each step of this fate conversion involves fine adjustments of the transcription and translation machineries as well as tight regulation of metabolism and migratory behaviors. Together, these data constitute the first in-depth analysis of a spontaneous cell fate conversion in the adult mammalian CNS.