This article is a continuation of the study of star-π-Hurewicz and strongly star-π-Hurewicz properties done in [Das et al.:On certain variations of π-Hurewicz property, Topology Appl. 251 (2018), 363β376]. We primarily consider and study the relative versions of star-π-Hurewicz and strongly star-π-Hurewicz properties. We study their relationships with the star-Hurewicz, strongly star-Hurewicz, star-π-Hurewicz, strongly star-π-Hurewicz and similar other properties. Few related games are also studied.