In this paper

the periodic systemx(τ+1)=f(τ

x)is considered

where τ∈(?)={τ_0+j:J=0

1

2

...}

x∈Rn

the n-vector f(τ

x)iscontinuous in x∈Rn

and f(τ+m

x)=f(τ

x)

m∈N+.Using fixed pointtheorems and Liapunov functions

we studied existence

uniqueness and stability ofperiodic solution of above system

and give some sufficient conditions to guaran-tee Zhe existence of the stationary oscillation and unique m-periodic solutionfor above system.