The nonsquare or James constant J(X) and the Jordan-von Neumann constant C-
NJ(X) are computed for two-dimensional Lorentz sequence spaces d((2))(w, q)
in the case where 2 less than or equal to q < infinity. The Jordan-von Neu
mann constant is also calculated in the case where 1 less than or equal to
q < 2. (C) 2001 Academic Press.