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This paper addresses a target-enclosing problem for multiple spacecraft systems by proposing a two-layer affine formation control strategy. Compared with the existing methods, the adopted two-layer network structure in this paper is generally directed, which is suitable for practical space missions. Firstly, distributed finite-time sliding-mode estimators and formation controllers in both layers are designed separately to improve the flexibility of the formation control system. By introducing the properties of affine transformation into formation control protocol design, the controllers can be used to track different time-varying target formation patterns. Besides, multi-layer time-varying encirclements can be achieved with particular shapes to surround the moving target. In the sequel, by integrating adaptive neural networks and specialized artificial potential functions into backstepping controllers, the problems of uncertain Euler …