1) This law cannot be applied to unilateral networks. A unilateral network has unilateral elements like diodes, transistors, etc., which do not have the same voltage-current relation for both directions of current.
2) This law is also not applicable for non-linear elements. Non-linear elements are those which do not have current exactly proportional to the applied voltage, that means the resistance value of these elements changes for different values of voltage and current. Examples of non-linear elements are thyristors, electric arc, etc.