A heterogeneous computer system is especially suitable for the execution of computer intensive applications consisting of various tasks. Due to fast networks and the Internet technology, in addition to enabling a high level of computer performances, it also has a capability of resource renewability. A high level of heterogeneity, timing variability and geographical distribution require a special attention regarding resource management. This dissertation presents mapping procedures in the mentioned conditions. The existing solutions of scheduling procedures represent the basis for solving mapping procedures. That is the aim of adjusting the notation α β γ to heterogeneous environment. The proposed HΩ model enables a thorough and more complete environment description. It includes application, platform, mapping, and resource owner/user parameters. The proposed MAMES algorithm is developed for scheduling tasks with precedence constraints on a set of uniform machines. According to simulation results, it shows better results than some other existing ones, but it also indicates possible high implementation requirements in real environment. On the other hand, the proposed heuristic mapping procedures are rather simple, and follow from the analysis of disadvantages of the existing procedures. Their goal is to achieve as short execution time and as uniform workload as possible. Two procedures (SM and BS) carry out matching separately from scheduling, whereas the other three (Gmm, PM and RCM) execute complete mapping of clustered tasks. An increase in number of parameters describing environment enables a better presentation and redundancy of parameters. The proposed principles of quasi-static and static-dynamic mapping are directed towards improving the control of environment dynamics. Short-term and long-term prediction procedures, as well as resource reservation, which are based upon multiple sporadic servers, have positive effects on remapping. Evaluation of mapping procedures and conditions is done in a simplified experimental environment on the basis of the proposed evaluation parameters. Experimental evaluation of the proposed procedures and the comparison to the existing ones show better results in the application execution. These results are the best for remapping with prediction and resource reservation, for the procedures of mapping clustered tasks.