We asked whether, in the first year of life, the infant brain can support the dynamic crossmodal interactions between vision and somatosensation that are required to represent peripersonal space. Infants aged 4 (n = 20, 9 female) and 8 (n = 20, 10 female) months were presented with a visual object that moved towards their body or receded away from it. This was presented in the bottom half of the screen and not fixated upon by the infants, who were instead focusing on an attention getter at the top of the screen. The visual moving object then disappeared and was followed by a vibrotactile stimulus occurring later in time and in a different location in space (on their hands). The 4-month-olds’ somatosensory evoked potentials (SEPs) were enhanced when tactile stimuli were preceded by unattended approaching visual motion, demonstrating that the dynamic visual-somatosensory cortical interactions underpinning representations of the body and peripersonal space begin early in the first year of life. Within the 8-month-olds’ sample, SEPs were increasingly enhanced by (unexpected) tactile stimuli following receding visual motion as age in days increased, demonstrating changes in the neural underpinnings of the representations of peripersonal space across the first year of life.