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We present an in-depth analysis of molecular excitation in 11 H₂ -bright planetary and protoplanetary nebulae (PN and PPN). From newly acquired K -band observations, we extract a number of spectra at positions across each source. H₂ line intensities are plotted on `column density ratio' diagrams so that we may examine the excitation in and across each region. To achieve this, we combine the shock models of Smith, Khanzadyan & Davis with the photodissociation region (PDR) models of Black & van Dishoeck to yield a shock-plus-fluorescence fit to each data set.

Although the combined shock + fluorescence model is needed to explain the low- and high-energy H₂ lines in most of the sources observed (fluorescence accounts for much of the emission from the higher-energy H₂ lines), the relative importance of shocks over fluorescence does seem to change with evolutionary status. We find that shock excitation may well be the dominant excitation mechanism in the least evolved PPN (CRL 2688 - in both the bipolar lobes and in the equatorial plane) and in the most evolved PN considered (NGC 7048). Fluorescence, on the other hand, becomes more important at intermediate evolutionary stages (i.e. in `young' PN), particularly in the inner core regions and along the inner edges of the expanding post-asymptotic giant branch (AGB) envelope. Since H₂ line emission seems to be produced in almost all stages of post-AGB evolution, H₂ excitation may prove to be a useful probe of the evolutionary status of PPN and PN alike. Moreover, shocks may play an important role in the molecular gas excitation in (P)PN, in addition to the low- and/or high-density fluorescence usually attributed to the excitation in these sources.