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In this paper, two elaborate numerical algorithms are presented for solving the Nani- Oguztoreli functional differential equations associated with cell-cycle specific cancer chemotherapy. The generalized cell-cycle specific cancer chemotherapy model of Nani- Oguztoreli contains discrete time delays which represent the times that the cancer cells spend in each cell-cycle phase. The model also takes into account that inter-cell cycle phase transition rate constants, recruitment of resting cells from the GO phase, and effect of chemotherapy drug on cells in each phase. The algorithms utilize a modified version of the Method of Steps algorithms. The constructed numerical schemes can be implemented in C++ or FORTRAN codes in order to generate clinically plausible simulations based on the model equations.