In this paper, the idea of using a multiple symbol obervation interval to improve error probability performance is applied to differential detection of MTCM(multiple trellis code modulation) with ${Pi}$/4 shift QPSK, 8DPSK and 16DPSK. We propose two types of sliding multiple symbol differential detection algorithm, type 1 and type 2. The two types of sliding detection scheme are examined and compared with conventional(symbol-by-symbol) detection and bolck detection with these modulation formats in an additive white Gaussian noise(AWGN) using the Monte Carlo simulation. We show that the amount of improvement over conventional and block detection depends on the number of phases and the number of additional symbol intervals added to the observation. Computer simulagtion results are presented for 2,4,8 states in AWGN channel.