As audio and video applications have proliferated on the Internet, caching multimedia objects in transcoding proxies has become an important technology for adapting the same multimedia object to meet diverse needs of various mobile appliances. In this paper, the problem of caching multimedia objects in transcoding proxies, i.e., determining the proper versions of the same multimedia object to be cached at selective nodes in a network such that the specified objective is achieved, is addressed. First, a novel model, which is formulated as an optimization problem by combining both transcoding cost and transmission cost in a cooperative way, is presented. Second, an optimal solution is derived for computing the optimal locations, which is also extended to solve the problem of optimally deciding the locations for placing a fixed number of versions of the same multimedia object in a network since caching more objects will generate great overhead as well. Finally, the performance of the proposed model is evaluated on different performance metrics through extensive simulation experiments.