The opening of the gravitational wave window by ground-based laser interferometers has made possible many new tests of gravity, including the first constraints on polarization. It is hoped that within the next decade pulsar timing will extend the window by making the first detections in the nano-Hertz frequency regime. Pulsar timing offers several advantages over ground-based interferometers for constraining the polarization of gravitational waves due to the many projections of the polarization pattern provided by the different lines of sight to the pulsars, and the enhanced response to longitudinal polarizations. Here we show that existing results from pulsar timing arrays can be used to place stringent limits on the energy density of longitudinal stochastic gravitational waves. Paradoxically however, we find that longitudinal modes will be very difficult to detect due to the large variance in the pulsar-pulsar correlation patterns for these modes. Existing upper limits on the power spectrum of pulsar timing residuals imply that the amplitude of vector longitudinal and scalar longitudinal modes at frequencies of 1/year are constrained: ${cal A}_{rm VL} < 4.1times 10^{-16}$ and ${cal A}_{rm SL} < 3.7times 10^{-17}$, while the bounds on the energy density for a scale invariant cosmological background are: $Omega_{rm VL}h^2 < 3.5 times 10^{-11}$ and $Omega_{rm SL}h^2 < 3.2 times 10^{-13}$.
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