The results of theoretical and experimental studies of Zeeman-perturbed nuclear quadrupole spin echo envelope modulations (ZSEEM) for spin 3/2 nuclei in polycrystalline specimens are presented. The response of the Zeeman-perturbed spin ensemble to resonant two pulse excitations has been calculated using the density matrix formalism. The theoretical calculation assumes a parallel orientation of the external r.f. and static Zeeman fields and an arbitrary orientation of these fields to the principal axes system of the electric field gradient. A numerical powder averaging procedure has been adopted to simulate the response of the polycrystalline specimens. Using a coherent pulsed nuclear quadrupole resonance spectrometer the ZSEEM patterns of the 35C1 nuclei have been recorded in polycrystaUine specimens of potassium chlorate, barium chlorate, mercuric chloride (two sites) and antimony trichloride (two sites) using the ~r/2-r--zr/2 sequence. The theoretical and experimental ZSEEM patterns have been compared. In the case of mercuric chloride, the experimental 3sCl ZSEEM patterns are found to be nearly identical for the two sites and correspond to a near-zero value of the asymmetry parameter, ~7, of the electric field gradient tensor. The difference in the ~ values for the two asC1 sites (7~0.06 and 7~0-16) in antimony trichloride is clearly reflected in the experimental and theoretical ZSEEM patterns. The present study indicates the feasibility of evaluating '1 for spin 3/2 nuclei in polycrystailine specimens from ZSEEM investigations.