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We solve the Killing spinor equations of 6-dimensional (1,0)-supergravitycoupled to any number of tensor, vector and scalar multiplets in all cases. Theisotropy groups of Killing spinors are $Sp(1)\cdot Sp(1)\ltimes \bH (1)$,$U(1)\cdot Sp(1)\ltimes \bH (2)$, $Sp(1)\ltimes \bH (3,4)$, $Sp(1) (2)$, $U(1)(4)$ and $\{1\} (8)$, where in parenthesis is the number of supersymmetriespreserved in each case. If the isotropy group is non-compact, the spacetimeadmits a parallel null 1-form with respect to a connection with torsion the3-form field strength of the gravitational multiplet. The associated vectorfield is Killing and the 3-form is determined in terms of the geometry ofspacetime. The $Sp(1)\ltimes \bH$ case admits a descendant solution preserving3 out of 4 supersymmetries due to the hyperini Killing spinor equation. If theisotropy group is compact, the spacetime admits a natural frame constructedfrom 1-form spinor bi-linears. In the $Sp(1)$ and U(1) cases, the spacetimeadmits 3 and 4 parallel 1-forms with respect to the connection with torsion,respectively. The associated vector fields are Killing and under someadditional restrictions the spacetime is a principal bundle with fibre aLorentzian Lie group. The conditions imposed by the Killing spinor equations onall other fields are also determined.

Spinorial geometry and Killing spinor equations of 6-D supergravity