In this dissertation work, a new modulation method for data communication is introduced, and its properties and various application areas are investigated. The proposed modulation method is based on the use of sinusoidal orthogonal waveforms (SOW``s). The modulated signal has constant envelope, continuity in magnitude and slope, and symbol orthogonality. Moreover, the binary SOW signal has the same bandwidth as that of minimum shift keying (MSK), and yields the performance that is identical to that of the optimal antipodal system. Also, we introduce a bandwidth efficient inphase/quadrature SOW (I/Q SOW) modulation method. The properties of the quadrature SOW (QSOW) signal is the same as those of the inphase SOW (ISOW) signal in the high-frequency range. Both signals do not interfere each other, when they are demodulated by sampling demodulation. Hence, by transmitting these signals simultaneously on the same channel capacity can be increased to twice that of the MSK system. In this dissertation, we first obtain the power spectral density and the autocorrelation function of the M-ary SOW signal. Then, we describe the structure of the M-ary SOW modem system, and investigate its performance. Further, we show that the binary SOW system yields the best performance among various M-ary SOW systems, and study its properties in detail. In addition, as applications of the SOW modulation method, we introduce a new spread spectrum method and a parallel communication system based on the SOW signal. To spread the narrow band data in an SOW spread spectrum system, we use an M-ary random sequence whose M symbols are mapped by SOW``s. The proposed system is in essence a hybrid form of the direct sequence/frequency hopping (DS/FH) system. It has a two-valued autocorrelation characteristic, always maintains phase continuity and constant envelope, and gives M-ary data modulation. Moreover, the distribution of the power spectrum of the spread signal is flat over the desired frequen...