The optical response of excited states is a key property used to probe photophysical and photochemical dynamics. Additionally, materials with a large nonlinear absorption cross-section caused by two-photon (TPA) and excited state absorption (ESA) are desirable for optical limiting applications. The ability to predict the optical response of excited states would help in the interpretation of transient absorption experiments and aid in the search for and design of optical limiting materials. We have developed an approach to obtain excited state absorption spectra by combining real-time (RT) and linear-response (LR) time-dependent density functional theory (TDDFT). Being based on RT-TDDFT, our method is aimed at tackling larger molecular complexes and materials systems where excited state absorption is predominantly seen and many time-resolved experimental efforts are focused. To demonstrate our method, we have calculated the ground and excited state spectra of H2+ and H2 due to the simplicity in the interpretation of the spectra. We have validated our new approach by comparing our results for butadiene with previously published results based on quadratic response (QR). We also present results for oligofluorenes, where we compare our results with both QR-TDDFT and experimental measurements. Because our method directly measures the response of an excited state, stimulated emission features are also captured; although, these features are underestimated in energy which could be attributed to a change of the reference from the ground to the excited state.