  The Kuo condition and the the second Kuo condition are known as criteria for
an r-jet to be V-sufficient in C^r mappings and C^{r+1} mappings, respectively.
In a previous paper we considered the notions of V-sufficiency of jets and
these Kuo conditions in the relative case to a given closed set, and showed
that the relative Kuo condition is a criterion for a relative r-jet to be
V-sufficient in C^r mappings and the second relative Kuo condition is a
sufficient condition for a relative r-jet to be V-sufficient in C^{r+1}
mappings. In this paper we discuss several conditions equivalent to the
relative Kuo condition or the second relative Kuo condition.
