In this study, we investigate two oscillators which have the same natural frequency, mutually coupled by N-type piecewise-linear negative resistor. In this system, according to the negative range of the coupling negative resistor, the various inter-esting synchronization phenomena which are in-phase, opposite phase and doublemode-like oscillations are observed. Especially, we show doublemode-like oscillations that are not observed until now in mutually coupled van der Pol oscillators with the smooth cubic characteristics, although the ones with same natural frequencies are coupled. And we show the differences of the phenomena between two oscillators coupled by the smooth cubic negative resistor and the ones coupled by the piecewise-linear negative resistor.