In this paper, we consider synchronization phenomena in coupled systems of piecewise constant oscillators. Both in-phase and anti-phase synchronization phenomena are observed in the oscillators, which are coupled by a voltage controlled current source (VCCS) with Signum-like characteristic. On the other hand, their co-existence is observed in the oscillators coupled by a VCCS with hysteresis characteristic. We analyze the stability of the synchronization phenomena in the coupled systems by using a fast calculation algorithm for the rigorous solutions. And we clarify the parameter regions of in-phase and anti-phase synchronization by deriving correlation coefficients. We suggest that the synchronization phenomena of the proposed systems qualitatively correspond to one of van der Pol oscillators coupled by passive elements. Some theoretical results are verified in the experimental circuits.