We consider the equation Delta u = 0 posed in Q := (0;+infty)imes Omega, Omega:= { x=(x',x_N)/ x'in R^{N-1}, x_N >0}, with the dynamical boundary conditionB(t,x',0)u_{tt} + A(t,x',0)u_t - u_{x_N} geq D(t, x',0)|u|^q on Sigma := (0,+infty) imes R^{N-1} imes {0} and give conditions on the coefficient functions A(t,x',0); B(t,x',0) and D(t;x',0) for the nonexistence of global solutions.