The purpose of this research is to develop algorithms for co-simulation using a dynamic phasor (DP) simulation program and an electromagnetic transient (EMT) simulator. The DP-EMT co-simulator offers flexibility in deciding the harmonic contents to be preserved in the dynamic phasor domain. Additionally, the co-simulator offers significant reduction in computational time of large networks compared with pure EMT simulators. The EMT simulator models a part of the network for which fast transients are prevalent and detailed modelling is necessary. The dynamic phasor simulator models the rest of the network, which allows larger simulation steps while keeping the accuracy during low-frequency transients. Specialized algorithms are developed for accurate mapping between instantaneous EMT samples and counterpart dynamic phasors. The thesis describes the mathematical foundations of the DP-EMT interface and provides demonstrations using illustrative examples. Several large networks are also studied to assess the accuracy of the interface and the performance in reducing the computational time. The findings of the thesis demonstrate that the co-simulation methods developed enable simulation of large electrical networks with adjustable accuracy in terms of retention of high-frequency transients via selection of the time-step ratio of the two simulators. The results also confirm that significant computational savings, which may even exceed an order of magnitude, may be expected in co-simulation of large networks. The findings of the thesis show a clear contribution to the advancement of transient simulation of complex modern power systems.