We report de magnetization measurements on the first available HgBa2Cu
O4+delta and HgBa2Ca2Cu3O8+delta (respectively Hg1201 and Hg1223) supe
rconducting single crystals, for fields applied both perpendicular and
parallel to the CuO2 planes. In the regime where the magnetization is
reversible and linear in logarithm of the applied field, we have used
the 3D London theory to determine the penetration depth lambda(ab) fo
r in-plane currents (lambda(ab)(0) similar or equal to 1300 +/- 100 An
gstrom for Hg1201 and similar or equal to 1500 +/- 100 Angstrom for Hg
1223). Using a relation derived from the anisotropic Ginzburg-Landau a
pproach, we have made an estimate of the anisotropy factor (gamma simi
lar or equal to 30 for Hg1201 and gamma similar or equal to 50 for Hg1
223). The results are in agreement with recent torque experiments on H
g1223.