Linear arrays of zinc meso-tetraarylporphyrin (ZnP), perylene-3,4-dicarboximide (PMI), and either naphthalene1,8:4,5-bis(dicarboximide) (NI) or pyromellitimide (PI) were synthesized and studied by ultrafast transient absorption spectroscopy. PMI was covalently linked in one of two orientations relative to ZnP. In one set of molecules, the 9 position of the perylene core is connected to the Para position of a meso-phenyl in ZnP to give ZnP-PMI-N-X, where X = NI or PI is attached to the imide nitrogen atom of PMI In the second set of compounds, the imide nitrogen atom of PMI is connected to the meso-phenyl in ZnP to give ZnP-N-PMI-X. where X = PI or H. Selective excitation of ZnP using 420 nm, 110 fs laser pulses in each molecule in toluene produces (ZnP)-Zn-1*, which intersystem crosses (ISC) to (ZnP)-Zn-3* with T = 2.3 ns. For ZnP-PMI-N-X, triplet energy transfer JET) from (ZnP)-Zn-3* to PMI is much faster than ISC, so that (ZnP)-Zn-3* is not observed by one-pump-one-probe transient absorption spectroscopy. Following its formation, the lowest excited triplet state of (PMI)-P-3* was excited with a 575 nm, 110 fs laser pulse to produce an upper excited triplet state, (3)**PMI. In ZnP-PMI-N-X, subpicosecond TET from (PMI)-P-3** re-populates 3*ZnP, which subsequently undergoes TET back to PMI with a rate of (7 ps)(-1). The same experiment carried out on ZnP-N-PMI-X reveals that the TET process (ZnP)-Zn-3*-N-->PMI-X - ZnP-N-3*-PMI-X occurs with a rate of (55 ns)-1. The nearly 8000-fold larger TET rate from 3*ZnP to PMI in ZnP-PMI-N-X relative to that in ZnP-N-PMI-X is a consequence of the larger pi-orbital coefficients at the 9 position in both the HOMO and LUMO of PMI relative to that on its imide nitrogen atom. This basic asymmetry allows optimization of energy and electron and/or hole transfer rates in large assemblies containing PMI for use in organic molecular electronics.