Abstract.    Parallel strategies based on compound disjoint Givens rotations are proposed for computing the main two factorizations that are used in the solution of seemingly unrelated regression and simultaneous equations models. The first factorization requires the triangularization of a set of upper-trapezoidals after deleting columns. The second factorization is equivalent to updating a lower-triangular matrix with a matrix having a block lower-triangular structure. Theoretical measures of complexity and examples are used for comparing and investigating the various parallel strategies.