GEARBI is a variant of the older GEAR package (predecessor to LSODE). It solves stiff and nonstiff systems, using BDF and Adams methods. The unique feature of GEARBI is that, in the case of stiff systems, it uses a block-iterative method, Block-SOR, to solve the linear systems that arise at each time step. GEARBI is designed for use on problems that arise from the spatial discretization of PDE systems, such that the resulting ODE system has a regular block structure. The original version of GEARBI, described and documented in [6], has been modified for the version here. The primary modification is in the treatment of the off-diagonal blocks of the Jacobian matrix. The new version assumes no structure for these blocks, but requires a user-supplied routine to compute matrix-vector products involving block-rows of the Jacobian, with the diagonal blocks excluded. The GEARBI solver is provided in separate single and double precision versions. Both have a driver routine, called DRIVBI. Documentation on the usage of GEARBI is provided in the initial block of comment lines in the source file. An example program, with a sample output, is also supplied for each precision.