The solar wind at the orbit of the Earth is usually strongly super‐Alfvénic and super‐fast, causing a bow‐shock to be formed upstream of the Earth's magnetosphere. We here present observational evidence that during 24 and 25 May 2002, the solar wind at the Earth was sub‐Alfvénic (with an Alfvén Mach number as low as 0.4 in the rest frame of the Earth) and was therefore sub‐fast for time periods of up to four hours. The low Alfvén Mach number implies that the Earth's bow‐shock disappeared and two Alfvén wings formed. These Alfvén wings are two structures on both the East and West side of the Earth's magnetosphere, where the solar wind plasma is decelerated and the magnetic field direction changes. We present observations of the Geotail spacecraft, which are consistent with Geotail entering the foot of one of these Alfvén wings. We estimate that these wings reached an extension of 600 RE. Even though Alfvén wings are present at several moons in the solar system (e.g., Io, Europa, Enceladus) and are likely to occur at some extrasolar planets, this is the first time that they are observed at the Earth. We also study how the Earth is affected by this transition from a super‐fast to a sub‐Alfvénic environment and how the Alfvén wings are affected by the constantly varying solar wind. The sub‐Alfvénic solar wind is due to very low density in the solar wind. While the solar wind Alfvén Mach number was very low, the magnetosphere was geomagnetically extremely quiet. Whereas the SYM‐H index indicates a recovery phase from a small to moderate magnetic storm; the AL and AU indices show no substorm activity. In addition, there was almost no auroral activity.