We introduce the notion of asynchrony immunity for cellular automata (CA), which can be considered as a generalization of correlation immunity in the case of boolean functions. The property could have applications in cryptography, namely as a countermeasure for side-channel attacks in CA-based cryptographic primitives. We give some preliminary results about asynchrony immunity, and we perform an exhaustive search of (3, 10)–asynchrony immune CA rules of neighborhood size 3 and 4. We finally observe that all discovered asynchrony-immune rules are center-permutive, and we conjecture that this holds for any size of the neighborhood.