A continuous operator T between two normed vector lattices E and F is called unbounded order-norm continuous whenever x α uo − → 0 implies Tx α → 0, for each norm bounded net (x α) α ⊆ E. Let E and F be two Banach lattices. A continuous operator T : E → F is called unbounded norm continuous, if for each norm bounded net (x α) α ⊆ E, x α un − → 0 implies Tx α un − → 0. In this manuscript, we study some properties of these classes of operators and investigate their relationships with the other classes of operators