In the present paper, the nature of the fragility of liquids with a developed H-bond network is investigated. It is shown that the effective activation energy of the shear viscosity eta and the fragility parameter defined as m=d log eta/d(Tg/T)|t=t+g are immediately connected with the average number nH(T) of the H-bond per molecule. The consistency of the macroscopic (m) and the microscopic [M=d(u(2)(0)/<u(-->2)>loc)/d(Tg/T)|T=T+8, where <u-->2>loc=<u-->2>anharm - <u-->2>harm] definitions of the fragility is established.