A TDS (X, f) is called N-accessible if for any and any N nonempty open subsets U1, U2, … UN of X there are N points x1 ε U1, x2 ε U2, … xN ε UN and a positive integer n such that : . A TDS (X,f) is called N-sensitive if there is a positive number τ such that in every nonempty open subset U of X there are N distinct points of U and a positive integer n with , .A TDS (X,f) is called (N1,N2)- everywhere chaotic if it is N1-sensitive and N2-accessible. We point out that there is a system which is (N1,N2)-everywhere chaotic, but it is not (N1 + 1, N2 )-everywhere chaotic for any positive integers N1 and N2.