Stochastic temporal logics have demonstrated their efficiency in the analysis of discrete-state stochastic models. In this paper we consider the application of a recently introduced formalism, namely the Hybrid Automata Stochastic Language (HASL), to the analysis of biological models of genetic circuits. In particular we demonstrate the potential of HASL by focusing on two aspects: first the analysis of a genetic oscillator and then the analysis of gene expression. With respect to oscillations, we formalize a number of HASL based measures which we apply on a realistic model of a three-gene repressilator. With respect to gene expression, we consider a model with delayed stochastic dynamics, a class of systems whose dynamics includes both Markovian and non-Markovian events, and we identify a number of relevant and sophisticated measures. To assess the HASL defined measures we employ the COSMOS tool, a statistical model checker designed for HASL model checking.