We study two types of specification properties - standard and initial - and extend them to CR-dynamical systems, where the dynamics are given by closed relations instead of continuous functions. Although these properties are often equivalent in classical settings, we show they can behave differently in this broader context. We define new specification-type properties for Mahavier dynamical systems and present several examples that highlight their differences. Each new property matches the classical specification property when applied to continuous functions. This is joint work with Iztok Banič, Ivan Jelić and Judy Kennedy