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In the present paper, we consider the bivariate version of reciprocal coordinate subtangent (RCST) and study its usefulness in characterizing some important bivariate models.  In particular, characterization results are proved for a general bivariate model whose conditional distributions are proportional hazard rate models (see Navarro and Sarabia, 2011), Sarmanov family and Ali-Mikhail-Haq family of bivariate distributions.  We also study the relationship between local dependence function and reciprocal subtangent and a characterization result is proved for a bivariate model proposed by Jones (1998).  Further, the concept of reciprocal coordinate subtangent is extended to conditionally specified models.