BeZnCdSe quaternaries, MgSe/BeZnCdSe superlattice (SL) and BeZnCdSe quantum well (QW) structures were grown on InP substrates by molecular beam epitaxy for the first time. As for a lattice-matched Be-0.08(Zn0.30Cd0.70)(0.92)Se sample, a single-peak photoluminescence (PL) spectrum was observed at the temperature range from 15K to room temperature. The PL peak wavelength and the full-width at half-maximum (FWHM) value at 15 K were 572 nm and 8.8 meV, respectively. PL measurements of MgSe/BeZnCdSe SL samples were observed single-peak emissions in the green-to-blue color range from 525 to 470 nm at 15 K with changing MgSe layer-thickness ratio from 0.20 to 0.60. As for the QW sample consisting of four BeZnCdSe QWs with a different well width, PL peaks corresponding to each QW were observed in the wavelength range from 459 to 561 nm at 15 E(. By fitting calculated transition energies in the QWs to the PL peak energies. the band offset ratio between the BeZnCdSe well and the MgSe/BeZnCdSe SL barrier was estimated to be DeltaE(c) : DeltaE(v) = 9 : 1.