The critical behaviour of the magnetic susceptibility χ of a spin−12 Ising system on a quadratic lattice in which the coupling constant along one of the lattice axes, J2, is very small in comparison with the coupling constant along the other axis, J1, is investigated on the basis of the series expansion of χ in the variables t1 = tanh (J1kT) and t2 = tanh (J2kT). It is shown that for t2 ⪡ 1, 1 − t1 ⪡ 1 the reduced susceptibility χ′ (kT/μ2)χ) behaves as χ′(t1, t2≃ χ′ (t1, t2 = 11−t1 ∑n = 0∞ bn0 (t21−t1)n, where the bn0 are constants. In the limit (t1, t2) → (1, 0), taken in such a way that the series Σnbn0 [t2(1 −t1)]n converges, χ'0 diverges through its first factor as the susceptibility of a l inear Ising chain. On the other hand, the two-dimensional nature of the system is displayed by the behaviour of χ'0 in the limit (t1,t2)→(τ, b−1(1 − τ))≠(1, 0), where b−1 is the radius of convergence of the power series Σnbn0xn. Numerical evidence suggests that in this limit χ′0 diverges as [1 - bt2/(1 - t1)]−p with b = 2.02 ± 0.03 and p = 1.77 ± 0.03. The exact value of b should be 2, as can be seen from the equation for the critical temperature in terms of the variables t1 and t2 ; that of p is most probably equal to the critical exponent of χ for the isotropic lattice, 74.