Final answer:
Two new nuclei form during the telophase of the cell cycle, which is the final stage of mitosis, characterized by the reformation of the nuclear envelope around each set of segregated genetic material.
Step-by-step explanation:
Two new nuclei form during the telophase of the cell cycle. Telophase is the final stage of mitosis, which follows interphase and includes prophase, metaphase, anaphase, and then telophase in that order. During telophase, the cell's duplicated genetic material is segregated into two distinct areas of the cell, and a nuclear envelope reforms around each set, thus creating two new daughter nuclei. Following this step, cytokinesis typically occurs, leading to the division of cytoplasm and the complete formation of two separate daughter cells.