When the application code is downloaded into the mobile device, it is important to provide authentication. Usually, mobile code execution is overlapped with downloading to reduce transfer delay. To the best of our knowledge, there has not been any algorithm to authenticate the mobile code in this environment. In this paper, we present two efficient code authentication schemes that permit overlapping of execution and downloading under the two cases: the first is when the order of transmission of code chunks is determined before the transmission and the second is when this order is determined during the transmission. The proposed methods are based on hash chaining and authentication trees, respectively. Especially, the latter scheme utilizes previously received authentication informations to verify the currently received chunk, which reduces both communication overhead and verification delay. When the application code consists of n chunks, communication overheads of the both schemes are 0(n) and verification delays of these two schemes are O(1) and O(log n), respectively.