We study the variational stability of an optimal control problem for a Volterra-type nonlinear functional-operator equation. This means that for this optimal control problem (Pɛ) with a parameter ɛ we study how its minimum value min(Pɛ) and its set of minimizers argmin(Pɛ) depend on ɛ. We illustrate the use of the variational stability theorem with a series of particular problems.