In this paper we consider the fuzzy and crisp multi mode resource-constrained project scheduling problem (F/C-MMRCPSP) with multiple execution modes for each activity. The objective function is the minimization of the project completion time. Heuristics based on Minslack priority rules are considered as initial solution procedures for this problem. Nevertheless, the NP-hard nature of the problem which is difficult to use to solve realistic sized projects makes necessary the use of heuristic and metaheuristics in practice. A global search metaheuristics taboo search algorithm (TSA) is proposed to solve this NP-hard problem. Two heuristic algorithms are developed to solve an F/C-MM-RCPSP. The first one is a minslack priority scheduling algorithm which includes a combination of an activity and a mode selection rule; the second one is a TSA. The solutions obtained by the former algorithm with the best activity and mode-priority rule combination are used as a baseline to compare those obtained by the latter. Finally, we present the results of our through computational study. A computational experiment is described, performed on a set of instances based on standard test problems from the PSPlib for the MM-RCPSPs. The algorithms are computationally compared, the results are analyzed and discussed and some conclusions are given.