### Description

We introduce the structure of generalised frame bundles, which generalises that of frame bundles with connection by keeping only the local part of the structure.

This definition is motivated by a Lagrangian field theory which we will present.

Its solution fields define on the 10-dimensional source manifold a structure of generalised frame bundle which satisfy further equations.

Some of these equations are shown to imply Einstein's equation in the case of a standard frame bundle and therefore can be used as a suitable generalisation thereof.