Using a density matrix formalism we derive a general expression for the resonant response of an ensemble of molecular aggregates to two optical pulses. The aggregates, which can be of arbitrary geometry, are described by a Frenkel exciton Hamiltonian including exciton-exciton interactions. A hierarchy of resonant coherent transient signals is generated having wave vectors sk(1)+(1-s)k(2), where k(i) is the wave vector of the ith pulse and s is an integer. General expressions for the differential pump-probe absorption spectrum D(omega;t(D)) (s=0) and the photon echo I-echo(t(D)) (s=-1) are presented for arbitrary pulse intensities. Applications are made to a linear chain of interacting Frenkel excitons with nearest neighbor exciton-exciton interaction A and exciton transfer J. Analytical expressions for D(omega;t(D)) and I-echo(t(D)) are obtained which are valid to third order in the aggregate-field interaction. The influence of the optically active red (blue) biexciton which detaches from the bottom (top) of the two-exciton band when A<-2J (A>2J) is investigated. Biexcitons appear as extra peaks in D(omega;t(D)) and as oscillations in I-echo(t(D)). Finite size effects are responsible for quantum beat oscillations in D(omega;t(D)) and long time oscillations in the echo decay. Quantum beats arise predominantly from the difference between the lowest one-exciton frequencies. Our theory successfully describes the salient spectral features in the pump-probe spectra of J-aggregates.