Ingram, \cite[Problem 6.56, p.81]{ingram2012introduction}, asked what can be said about the Property of Kelley in the generalized inverse limit space $\varprojlim{X_i,f_i}$ where ${f_i}$ is a sequence of upper semi-continuous bonding functions. In this work, we give conditions on the projection maps from the graph of the functions $f_i$ to the domain and co-domain such that if the first factor space, in the case of Theorem 2.2, or all factor spaces, in the case of Theorem 2.4, have the Property of Kelley then the generalized inverse limit space $\varprojlim{X_i,f_i}$ has the Property of Kelley. Furthermore, we present examples demonstrating that if any condition is dropped then the inverse limit space may not have the Property of Kelley. These results also answers several questions by Charatonik, Mena and Roe \cite{Charatonik2020}. This is joint work with Faruq Mena and Robert Roe.