Submitted to Physical Review Letters. The article of record may be found at http://dx.doi.org/10.1103/PhysRevLett.76.587.We have measured proton and deuteron virtual photon-nucleon asymmetries Ap2 and Ad2 and structure functions gp2 and gd2 over the range 0.03<x<0.8 and 1.3<Q2<10(GeV/c)2 by inelastically scattering polarized electrons off polarized ammonia targets. Results for A2 are significantly smaller than the positivity limit R‾‾√ for both targets. Within experimental precision the g2 data are well described by the twist-2 contribution, gWW2. Twist-3 matrix elements have been extracted and are compared to theoretical predictions.Work supported in part by Department of Energy contract DE-AC03-76SF00515