A space $X$ is said to be neighborhood star-Lindel\"of $\Cal U$ of $X$ there exists a countable subset $A$ of $X$ such that for every open $O\supseteq A$, $X=St(O,\Cal U)$. In this paper, we continue to investigate the relationship between neighborhood star-Lindel\"of spaces and related spaces, and study topological properties of neighborhood star-Lindel\"of spaces in the classes of normal and pseudocompact spaces. if for every open cover