The influence of a layered aperiodic modulation of the couplings on th
e critical behaviour of the two-dimensional Ising model is studied in
the case of marginal perturbations. The aperiodicity is found to induc
e anisotropic scaling. The anisotropy exponent z, given by the sum of
the surface magnetization scaling dimensions, depends continuously on
the modulation amplitude. Thus these systems are scale invariant but n
ot conformally invariant at the critical point.