Syntheses, heat-treatments, structures and the superconducting propert
ies of the first four members of the homologous series HgBa2Can-1CunO2
n+2+delta are presented and discussed. Syntheses under high pressure s
eem to yield samples which contain less than 5% impurities. The struct
ural characterization has been carried out by X-ray diffraction, elect
ron microscopy and neutron diffraction. Heat-treatments in oxidizing a
tmospheres usually increase T(c). The member with n = 2 does not follo
w this rule because the as-prepared sample (T(c) = 104 K) seems to be
overdoped. Heat-treatment in N2 at 250-degrees-C for 10 h induces an i
ncrease in T(c) to 123 K. Additional heat treatment under N2 (400-degr
ees-C, 18 h) decreases T(c) to 110 K. In Hg-1212 superconductivity exi
sts in underdoped and overdoped regions.