In this paper, we propose a direct-sequence spread spectrum multiple access (DS/SSMA) unslotted ALOHA system with two user classes and analyze the throughput of the proposed system. Mobile stations (MSs) are divided into two classes according to its priority or traffic characteristics such as delay-intolerant and delay-tolerant. Different permission probabilities are assigned to each class so that the appropriate quality of service can be provided. We assume that the generation of class 1 and 2 messages are Poisson distributed and the message is divided into several packets before transmission. The system is modeled as a two-dimensional Markov chain under the assumption that the number of packets transmitted immediately by both user classes is geometrically distributed and the packet length is constant. We calculate the packet success probability and the throughput as a function of the signal-to-noise ratio (SNR) during packet transmission, considering the number of overlapped class 1 and 2 messages and the amount of their time overlap. Moreover, we show that the proposed system differentiates user messages according to class and maintains a high throughput even under heavy traffic conditions using access control based on the channel load.