This paper deals with the computation of the reducing subspace associated with the rightmost part of the spectrum of a large matrix pencil A-λ B with B = diag(I,0). Two variants of the Jacobi-Davidson method are discussed and developed. One is based on the Euclidean inner product and the second on the semi-inner product induced by B. Both versions use real arithmetics and incorporate an efficient deflation procedure. Numerical results are reported.