The critical behaviour of the reduced magnetic susceptibility X'≡( kT μ 2 )X of spin- 1 2 Ising systems on d-dimensional cartesian lattices in which the coupling constants along d-1 lattice axes, J 2,… J d, are much smaller than the coupling constant along the remaining lattice axis, J 1, and in which some of the J i are negative, is investigated on the basis of the series expansion for X' in the variables t i = tanh βJ i , i = 1,… d. For 1 + t 1 《 1 ; |t 2 |,… |t d | 《 1 , X' is found to behave as X'(t 1 ,…t d )≈X' 0 (t 1 ,…t d )≡( 1+t 1 ) ∑ n 2=o ∞ … ∑ n d=o ∞ c n 2…n d 0 Φ i=2 d t 1 1+t 1 , where the c n2… n d0 are constants. In the limit ( t 1,… t d)→(-1, 0,…0), taken in such a way that the power series in this expression remains convergent, X' 0 behaves through the factor 1+ t 1 as the susceptibility of the antiferromagnetic linear Ising chain. The d-dimensional nature of the system is contained in the power series. It is rigorously shown that X' 0 = 1 2 ( 1+<σ 1 σ 2 ) 0 , where < σ 1 σ 2 is the spin-spin correlation function for nearest neighbours along the first lattice axis, and ( ) 0 is the leading-order term for ( t 1, t 2,… t d)→(−1, 0,…0) of the quantity within the brackets. Using this relation it is shown that for the quadratic lattice with ( t 1, t 2) ≈ (−1, 0) X' 0 is given by X' 0 = ( 1+t 1 ) 1 π ƒ 0 π 2 1 − 4 ( t 2 1 + t 2 ) 2sin 2Ψ 1 2 . The fact that the integral, and hence X' 0, displays the same critical behaviour as the internal energy is discussed in connection with the critical behaviour of X' for antiferromagnetic Ising systems in general. A numerical analysis indicates that for the quadratic lattice with t 1 ↑ 1, t 2 ↑ 0 the critical behaviour of the leading-order term of X' is also similar to that of the internal energy. Finally, the first-order correction X' 1 on X' 0 is calculated explicitly for the quadratic lattice with ( t 1, t 2) ≈ (-1, 0), and the region of validity of the approximation X'≈ X' 0 is discussed.