The John–Nirenberg spaces JNp are generalizations of the space of bounded mean oscillation BMO with JN∞= BMO . Their vanishing subspaces VJNp and CJNp are defined in similar ways as VMO and CMO, which are subspaces of BMO. As our main result, we prove that VJNp and CJNp coincide by showing that certain Morrey type integrals of JNp functions tend to zero for small and large cubes. We also show that JNp,q(Rn) = Lp(Rn) / R , if p= q .