The operator T from a domain D into the space of measurable functions is called a nonanticipating (causal) operator if the past information is independent from the future outputs. We will study the solution x(t) of a nonlinear operator differential equation where its changes depends on the causal operator T, and semigroup of operator A(t), and all initial parameters (t₀, x₀) . The initial information is described x(t)=φ(t) for almost all t ≤t₀ and φ(t₀₎ =φ₀. We will study the nonlinear variation of parameters (NVP) for this type of nonanticipating operator differential equations and develop Alekseev type of NVP.