In this work, we determined the diversity and dynamics of the gut virome of infants during the first year of life. Fecal samples were collected monthly, from birth to one year of age, from three healthy children living in a semi-rural village in Mexico. Most of the viral reads were classified into six families of bacteriophages including five dsDNA virus families of the orderCaudovirales, withSiphoviridaeandPodoviridaebeing the most abundant. Eukaryotic viruses were detected as early as two weeks after birth and remained present all along the first year of life. Thirty-four different eukaryotic virus families were found, where eight of these families accounted for 98% of all eukaryotic viral reads:Anelloviridae,Astroviridae,Caliciviridae,Genomoviridae,Parvoviridae,Picornaviridae,Reoviridaeand the plant-infecting viruses of theVirgaviridaefamily. Some viruses in these families are known human pathogens, and it is surprising that they were found during the first year of life in infants without gastrointestinal symptoms. The eukaryotic virus species richness found in this work was higher than that observed in previous studies; on average between 7 and 24 virus species were identified per sample. The richness and abundance of the eukaryotic virome significantly increased during the second semester of life, probably because of an increased environmental exposure of infants with age. Our findings suggest an early and permanent contact of infants with a diverse array of bacteriophages and eukaryotic viruses, whose composition changes over time. The bacteriophages and eukaryotic viruses found in these children could represent a metastable virome, whose potential influence on the development of the infant’s immune system or on the health of the infants later in life, remains to be investigated.