We present moderate- and high-resolution infrared spectroscopy of the peculiar eruptive variable V838 Mon, which underwent a series of remarkable outbursts in early 2002. During the period covered by our observations, 2002 December–2003 December, the near-infrared spectrum continued to show many of the characteristics of a very cool supergiant. However, throughout this period the spectrum also revealed strong and variable SiO first overtone emission, and Paβ emission. The 2003 December spectrum contained a series of Ti I lines with inverse P Cygni profiles. This is clear evidence that some material is falling inward towards the star.