Ambient calculus is a process algebra developed for describing mobile processes. Ambients represent the substances of movement and the fields of the ambients themselves. Having this hierarchy, it can model various kinds of mobile computation. Equational relation for ambient calculus “Contextual Equivalence” were proposed regarding the names of ambients observed from the environment. This relation is, however, not strong as “testing equivalence” so that it can identify the processes which have different properties. This paper proposes equational relations for ambient calculus by which we can distinguish processes that the existing equivalence identifies.