We modify the concept of SL-homomorphism introduced by K.P. Shum, P. Zhu and N. Kehayopulu [7] for directed posets. Since every directed poset can be converted into an algebra called a directoid, we investigate the relationship between our homomorphisms and these of directoids. We point out that no modification of SL-congruences is necessary since congruences induced by our homomorphisms are just that of directoids.