Definition 4.1 The periodic solution Ψ( t ) : $^{R}$→ D of (2.1) is said to be orbitally stable if for every ϵ > 0 , there corresponds δ = δ ( ϵ ) > 0 such that dist ( x ( t, 0 , x$_{0}$ ) , η ) < ϵ, for all t ≥ 0 , provided dist ( x$_{0}$, η ) < δ and x$_{0}$ / ∈ ∪ $_{i}$c $^{+}$(Ψ( θ$_{i}$ ) , δ ) , for i = 1 , . . . , m, where m is the number of points Ψ( θ$_{i}$ ) ∈ Γ \ ∂ Γ . The point x$_{0}$ is not considered in regions c $^{+}$(Ψ( θ$_{i}$ ) , δ ) , i = 1 , . . . , m, since solutions which start there move continuously on a finite interval, while Ψ( t ) experiences a non-zero jump at t = θ$_{i}$ and this violates the continuity in initial value, in general. In the same time, we take into account any region adjoint to points of ∂ Γ , since the jump of Ψ( t ) is zero there and, consequently, the continuous dependence in initial value is valid for all near points. Definition 4.2 The solution Ψ( t ) : R$_{+}$ → D of (2.1) is said to have asymptotic phase property if a δ > 0 exists such that to each x$_{0}$ satisfying dist ( x$_{0}$, η ) < δ and x$_{0}$ / ∈ ∪ $_{i}$c $^{+}$(Ψ( θ$_{i}$ ) , δ ) , for i = 1 , . . . , m, there corresponds an asymptotic phase α ( x$_{0}$ ) ∈ $^{R}$with property: for all ϵ > 0 , there exists T ( ϵ ) > 0 , such that x ( t + α ( x$_{0}$ ) , 0 , x$_{0}$ ) is in ϵ -neighborhood of Ψ( t ) in B − topology for t ∈ [ T ( ϵ ) , ∞ ) . Let us consider the following system, which will be needed in the following lemmas and theorem where A ( t ) and B$_{i}$ are n × n function-matrices, A ( t + ω ) = A ( t ) , for all t ∈ $^{R}$and there exists an integer p such that ζ$_{i}$$_{+}$$_{p}$ = ζ$_{i}$ + ω and B$_{i}$$_{+}$$_{p}$ = B$_{i}$, for all i ∈ $^{Z}$. Lemma 4.1 Assume that system (4.31) has a simple unit characteristic multiplier and the remaining n − 1 ones are in modulus less than unity. Then, the system (4.31) has a real fundamental matrix X ( t ) , of the form where P ∈ P C $^{1}$( $^{R}$, θ ) is a regular, ω -periodic matrix, and B is an ( n − 1) × ( n − 1) matrix with all eigenvalues have negative real parts. X ( t ) = P ( t )    1 0 0 exp ( Bt )    , (4.32) $_{x}$′ = A ( t ) x, Δ x | t = ζ$_{i}$ = B$_{i}$u, (4.31) z ′ = Λ z. (4.33) Proof. Denote the matrix X ( t ) , X (0) = I, as fundamental matrix of system (4.31). There exists a matrix B$_{1}$ such that the substitution x = P ( t ) z, where P ( t ) = X ( t ) exp( − B$_{1}$t ) , transforms (4.31) to the following system with constant coefficient [1], The matrix exp(Λ ω ) has a simple unit eigenvalue and remaining ( n − 1) ones are in modulus less 21