A derivation of density-functional response theory is presented which is based directly on the Runge-Gross theorem and does not invoke the action formalism and thus does not violate causality requirements in time. Working equations to treat linear and nonlinear response properties of electronic systems by time-dependent density-functional theory in the frequency domain are given. Efficient noniterative methods to calculate dynamic hyperpolarizability tensors of molecules for arbitrary frequency combinations are presented. With the introduced methods, hyperpolarizabilities of benzene and stilbene derivatives are investigated. The results show that the influence of substituents on the frequency-dependent hyperpolarizability is well described by time-dependent density-functional theory at the adiabatic local density level. Inspection of the linear and nonlinear response of the electron density shows the importance of screening effects for the response properties of larger molecules on electric fields and electromagnetic radiation.