  This paper is concerned with the holonomy of a class of spaces which includes
Landsberg spaces of Finsler geometry. The methods used are those of Lie
groupoids and algebroids as developed by Mackenzie. We prove a version of the
Ambrose-Singer Theorem for such spaces. The paper ends with a discussion of how
the results may be extended to Finsler spaces and homogeneous nonlinear
connections in general.
