Experimental results showing huge negative differential conductance in gold-hydrogen molecular nanojunctions are presented. The results are analyzed in terms of two-level system (TLS) models: it is shown that a simple TLS model cannot produce peaklike structures in the differential conductance curves, whereas an asymmetrically coupled TLS model gives perfect fit to the data. Our analysis implies that the excitation of a bound molecule to a large number of energetically similar loosely bound states is responsible for the peaklike structures. Recent experimental studies showing related features are discussed within the framework of our model.