The essential features of the near-field approximation for strong gravitational fields are elucidated by developing the approximation (i) in first order for quasistatic systems; (ii) to arbitrary order for nonrotating systems with axial symmetry; and (iii) by sketching the approximation for rotating, axially symmetric systems. The restrictions, placed by Einstein's equations, on the time dependence of the "multipole moments" of a system which is isolated from other bodies of empty space are exhibited. These restrictions are statements of the global conservation of energy and linear momentum. In Newtonian theory they would state that, for an isolated system, $\left(\frac{d}{\mathrm{dt}}\right)A_0=0\mathrm{}$ and $\left(\frac{d^2}{d{t}^2}\right){\mathbf{A}}_1=0\mathrm{}$ where $A_0$, ${\mathbf{A}}_1$ are multipole moments. The principal assumption made in this paper is simply that a near-field zone exists for the systems which we consider (i.e., $\frac{L}{\lambda }<1\mathrm{}$). We do not, in any sense, assume that the gravitational fields are weak. The contracted Bianchi identity ${{G_0}^{\nu }}_{;\nu }\equiv 0$ plays a crucial role in the analysis since it implies, for a quasistationary system, that if the empty-space field equations $G_{\mu \nu }=0\mathrm{}$ are obeyed in order $n$, then ${\left[{\mathrm{}(-g)\mathrm{}}^{\frac{1}{2}}{G_0}^i\right]}_{,i}=0\mathrm{}$ is obeyed in order $n+1\mathrm{}$. This in turn implies the existence of a vanishing surface integral which restricts the time dependence of the quasistationary field in each order. It is shown that there are close similarities between strong gravitational fields and electromagnetic fields in the near-field approximation. For example, just as the first effect of a quasistatic electromagnetic field is to induce a magnetic field, so the first effect of a quasistatic gravitational field is to induce a magneticlike field, whose potentials are $g_{0i}$.

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