  Measurement-Induced NonLocality was introduced by Luo and Fu (Phys. Rev.
Lett. \textbf{106}, 120401,(2011)) as a measure of nonlocality in a bipartite
state. In this paper we will discuss monogamy property of measurement-induced
nonlocality for some three- and four-qubit classes of states. Unlike discord,
we find quite surprising results in this situation. Both the GHZ and W states
satisfy monogamy relations in the three-qubit case, however, in general there
are violations of monogamy relations in both the GHZ-class and W-class states.
In case of four-qubit system, monogamy holds for most of the states in the
generic class. Four qubit GHZ does not satisfy monogamy relation, but W-state
does. We provide several numerical results including counterexamples regarding
monogamy nature of measurement induced nonlocality. We will also extend our
results of generalized W-class to n-qubit.
