A tool-support apparatus for attachment to a grinding machine, in particular to a wet grinding machine, which has at least one grinding disc arranged on a rotatably drivable grinding-disc shaft and a machine frame or housing in which the grinding-disc shaft is supported. The tool-support apparatus has a tool-support, which can be secured on a machine frame or housing of the grinding machine, for the support during the grinding process of a tool that is to be ground, and an arresting apparatus for securing the tool support on the machine frame or housing. The tool-support can be secured on the machine frame or housing in such a way that it can be swivelled about the grinding-disc shaft or about a swivel axis parallel to the grinding-disc shaft and can be arrested by way of the arresting apparatus in a plurality of angular positions.