We present a joint experimental and theoretical investigation of the linear and nonlinear optical response of butadiyne-linked zinc porphyrin oligomers. Efficient overlap between the chromophores leads to a large red-shift of the Q absorption band together with a splitting of the B band into two components when increasing the chain length from one to two repeating porphyrin units. Ultrafast pumb-probe measurements performed on these compounds show several well-defined features, associated with singlet excited state absorption. We also find clear evidence for the formation of longer-lived triplet excitons, resulting from very efficient singlet-triplet intersystem crossing processes, For the monomers, the assignment of the observed linear and photoinduced absorption features is supported by a Configuration Interaction description of the singlet and triplet excited states. In the case of the porphyrin dimer, agreement with the experimental results can only be obtained by considering a sizable cumulenic contribution in the excited-state geometry used as input for the CI calculations. The potential of porphyrin systems for Reverse Saturable Absorption and Nonlinear Optics is emphasized.