The large zero-field splitting of rigid biradicals makes them important candidates for spin probes of phospholipid membranes. Here we develop an electron spin resonance line-shape model for such probes on the basis of the stochastic Liouville equation. Particular emphasis is given to the slow-diffusional regime, characteristic of bilayers in the gel phase. The theory is employed to study the line shapes of bis(verdazyl) biradicals, incorporated into oriented multibilayers of dimyristoylphosphatidylcholine. Computer simulations of the angular-dependent spectra provide the orientational distribution functions and rotational correlation times of the spin probes. They occupy two different sites in bilayer membrane. The orientational distribution of the spin probes is related to the structure of the phospholipid phases. In the L beta' phase the hydrocarbon chains are uniformly tilted by delta = 23 degrees with respect to the bilayer normal. For the P beta' phase we observe a random distribution of tilt angles from delta = 0 degree to delta = 19 degrees, indicating that the chains orient perpendicular to the local (rippled) bilayer surfaces. This structure has not been established previously. In agreement with other studies we find no tilt for the L alpha phase. The order parameters of the hydrocarbon chains increase with decreasing temperature, jumping from S less than or equal to 0.6 to S greater than or equal to 0.8 at the main transition. From the rotational correlation times of the spin probes, intrinsic bilayer viscosities of 0.08 P less than or equal to eta less than or equal to 20 P (50 degrees C greater than or equal to T greater than or equal to 1 degree C) are determined. An Arrhenius plot provides activation energies of the viscous flow. The values increase from Evisc approximately 10 kcal/mol in the L alpha phase to Evisc approximately 18 kcal/mol in the L beta' phase.