Dr.U.P.Verma, Dr. Samar Upadhyay, Mr. Sanjay Patsaria, Dr. Uma Shankar Sharma for their encouragements, valuable suggestions and appreciations of the work done. My heartily feelings of obligations are due to my parents for their inspiration and blessings, which provided me great energy for successful completion of this work. . I am grateful to my younger brother who always encouraged me and gave whole hearted support. *Chapter 1 introduces the concept of wireless networks and explains the different goals of IEEE 802.11 and IEEE802.15.4 wireless networks . *Chapter 2 represents survey of literature related to binary exponential backoff. *Chapter 3 explains the medium access mechanisms of both standards. *Chapter 4 details the differences between IEEE802.11 and IEEE802.15.4 with regards to radio characteristics. *Chapter 5 describes main work done in this thesis related to binary exponential backoff and non-overlapping binary exponential backoff algorithm. A comparative study of the results in both the cases is discussed in length.