Three-dimensionality in wakelike or jetlike free mixing may stem from initial geometric configurations, nommiformities in flow variables over a cross section, or boundary conditions along the flow. These may be generated by bodies at angle of attack, nonaxisymmetric bodies, mixing of nonaxisymmetric jets with an outer flow, finite wings, or more artificial means. This paper is devoted to studies bearing on such configurations. The first section deals with the general mathematical model, in which the boundary layer approximations are used, and with methods of solution. Laminar and turbulent flow, compressibility, unsteadiness, and streamwise pressure gradients are admitted initially. The flux forms of the equations are given. Algebraic integrals of the energy equations and the diffusion (frozenflow) equations are obtained. A simplification of the convective terms, roughly corresponding to the Oseen approximation, is used in the asymptotic downstream region. The second section contains explicit solutions for specific configurations, in particular for flows whose initial isovels are of elliptic shape. These flows may be wakelike or jetlike. Compressibility is admitted; however, the flows must have uniform pressure and must be steady. The final section deals with interpretation and evaluation of the results. Nomenclature associated with dissociation and ionization energies eccentricity h = static enthalpy (h -H = stagnation enthalpy, H = h + ^2/2 £2 = [l + 4s]-1 K = pure constant of order 10 ~2 L = constant characteristic length [see Eq. (26)] Le = Lewis number m = non-negative integer, ra = 0,1,2 ... Pr = Prandtl number Mi = gram-mole weight of species i R Q = universal gas constant Q = see Eq. (14a) s^i = transformed axial coordinate t = time T = absolute temperature u = axial velocity component u = axial velocity defect (u = u e -u) v,w = crossflow velocity components (see Fig. 1) Wi = net rate of production of species i x = axial coordinate y,z = cross-plane coordinate components (see Fig. 1) on = mass friction of species i 8 = viscous layer thickness §j = viscous layer thickness in the plane z -0 5 2 = viscous layer thickness in the plane y = 0 dm = minimum transform viscous layer thickness e = measure of the initial eccentricity [see Eq. (23)] e v = turbulent eddy viscosity ,7^ = transformed normal coordinate tj s = value of rj when y = 8 A/ = vibrational energy of species j Pr cr,