In recent years, the adoption of Software as a Service (SaaS) cloud services has surpassed that of Infrastructure as a Service (IaaS) cloud service and is now the focus of attention in cloud computing. The cloud market is becoming highly competitive owing to the increasing number of cloud service providers (CSPs), who are likely to exhibit different cloud capacities, i.e., the cloud market is heterogeneous. Moreover, as different users generally exhibit different Quality of Service (QoS) preferences, it is challenging to set prices for cloud services of good QoS. In this study, we investigate the price competition in the heterogeneous cloud market where two SaaS providers, denoted by CSP₁ and CSP₂, lease virtual machine (VM) instances from IaaS providers to offer cloud-based application services to users. We assume that CSP₁ only has M/M/1 queue of VM instances owing to its limited cloud resources, whereas CSP₂ has M/M/∞ queue of VM instances reflecting its adequate resources. We consider two price competition scenarios in which two CSPs engage in two games: one is a noncooperative strategic game (NSG) where the two CSPs set prices simultaneously and the other is a Stackelberg game (SG) where CSP₂ sets the price first as the leader and is followed by CSP₁, who sets the price in response to CSP₂. Each user decides which cloud services to purchase (if purchases are to be made) based on the prices and QoS. The NSG scenario corresponds to the practical cloud market, where two CSPs with different cloud capacities begin to offer cloud services simultaneously; meanwhile, the SG scenario covers the instance where a more recent CSP plans to enter a cloud market whose incumbent CSP has larger cloud resources. Equilibrium is achieved in each of the scenarios. Numerical results are presented to verify our theoretical analysis.