Summary: We calculate the characteristic of monotonicity of Orlicz-Lorentz function spaces \(\Lambda_{\Phi ,\omega}\). Since degenerate Orlicz functions \(\varphi\) and degenerate weight functions \(\omega\) are also admitted, these investigations concern the widest possible class of Orlicz-Lorentz function spaces. These results concern both cases, infinite and finite non-atomic measure spaces, although in the case of a finite measure the results are much more interesting. Let us recall that calculating the characteristic of monotonicity of a Banach lattice is of great interest because of the result of A. Betiuk-Pilarska and S. Prus [J. Math. Anal. Appl. 342, No. 2, 1271–1279 (2008; Zbl 1156.46018)] stating that, if a Banach lattice \(X\) has this characteristic strictly smaller then 1 and \(X\) is weakly orthogonal, then it has the weak fixed point property.