Nonlinear particle dynamics is studied both in current sheets and near neutral lines. The parameter governing particle chaos in a current sheet with a constant normal component, Bn, is κ=(Rmin/ρmax)1/2, where Rmin is the minimum field line radius of curvature and ρmax is the maximum gyroradius. In such a current sheet, motion can be viewed as a combination of a component normal to the current sheet and a tangential component. The parameter κ represents the ratio of the characteristic time scale of the normal component to the tangential, and thus, particle chaos is maximized for κ∼1. For κ≪1, the slow motion preserves the action integral of the fast motion, Jz, except near the separatrix, the phase space boundary separating motion that crosses the current sheet midplane from that which does not. Near a linear neutral line, it is found that the parameter bn, which is the ratio of the characteristic vertical and horizontal field strengths, rather than κ governs particle chaos. In the limit bn≪1, the slow motion again preserves Jz, and Jz has the same analytic form as in a constant Bn current sheet. In the limit of bn≪1, the structure of x-px phase space is controlled by the stable and unstable manifolds associated with the unstable fixed point orbit at (x,px)=(0,0), and this structure lies along a contour of constant Jz.