Modeling the dynamics of ecological systems is the most useful way to un- derstand the complexity of nature. In particular, mathematical model describes interactions between biological components such as predation, competition and parasitism. Host-parasitoid interactions and host-predator interactions constitute to a very important class of consumer resource dynamics. Discrete-time and continuous- time models, starting from the seminal work of Nicholson-Bailey and Lotka- Volteera, are traditions for such interactions. Host-Parasitoid-Predator models address the life cycles of three interacting species of insects: a host, a parasitoid and a predator. Biological control of insect pests is characterized by a persistent, strong reduction in the pest population following the introduction of natural enemies. As a result, a low and stable- equilibrium pest population is the desirable outcome in pest control. One reason why host-parasitoid-predator systems continue to receive much attention is their potential for biological control, where parasitoids and predators are introduced to reduce the host population of a pest on agricultural crops. A fundamental area of research in population ecology is to elucidate mecha- nisms that can account for the stability and realism. This thesis investigates some of these mechanisms and is divided into two parts. The first part of the thesis introduces a continuous-time approach to model host-parasitoid-predator popu- lations showing that host-parasitoid-predator interactions can result in damped oscillations before reaching the asymptotically stable co-existence equilibrium point where non-specialist parasitoid is introduced in the model. However, a modification of that model is necessary since the parasitoids are recognized by the hosts they parasitize and where their offspring develop. The second part of the thesis investigates the exact age stage at which hosts are parasitized. Furthermore, egg parasitoids exhibit a greater rate of establish- ment than other parasitoid guilds and predators tend to be less host-specific than parasitoids. Using this formalism, results connecting the stability of the host- parasitoid-predator interaction with Type I functional response are derived.