The purpose of the present paper is to address the problem of proving blowup of solutions for the following nonlinear wave equation
where is a complex-valued wave field, the operator is defined via its symbol and the symbol stands for convolution on . The authors establish the following result: any spherically symmetric initial data with negative energy gives rise to a solution of (1) that blows up within a finite time, more precisely for some . Moreover, the authors consider more general Hartree-type nonlinearities. As an application, they exhibit instability of ground solitary waves at rest if .