In order to gain an insight into the primary phase selection and solidification structure formation while undercooled eutectic alloys solidify, Ni100-xPx (x=18, 19, 19.6, 20, 21, atomic percent) alloy melts are undercooled to different temperatures below the equilibrium liquidus. The recalescence behavior associated with rapid solidification is monitored by a high-speed infrared pyrometer, and the solidification structure is analyzed systematically. When α-Ni/Ni3P regular eutectic forms as the primary phase during rapid solidification, single recalescence event takes place. In the resulting anomalous eutectic, fine granular grains of α-Ni are distributed uniformly in the Ni3P matrix. When the primary phase is one of the eutectic phases, however, there is a second recalescence event following the first one, resulting from nucleation of the other phase in the remaining liquid and the subsequent rapid eutectic growth. In this case, there are two types of granular grains whose sizes are significantly different from those in the anomalous eutectics. Finally, a coupled growth zone of eutectics is determined. At large undercoolings, α-Ni rather than Ni3P solidifies as the primary phase even in the Ni-P hyper-eutectic alloys due to its rapider growth kinetics.