Indigenous species of the tribe Triticeae and tribe Bambuseae, Gramineae, distributed in Japan are thought to be highly interesting and useful from the viewpoint of the genetic resources. This paper briefly reviews and discusses firstly general aspects of the cross compatibility that especially tended to appear in distant cross combinations, and secondly hybridization barriers with relation to the biological species concept. The aspects of the cross compatibility that are discussed testified in the hybridization investigation of the interspecific and intergeneric cross combinations that were made between species in the two tribes. The hybridization barrier between genera of the tribe Bambuseae was shown to be low. Species of Sasa group hybridized successfully with Phyllostachys bambusoides and with Sinobambusa tootsik, both distantly related species of Bambuseae. On the other hand, in the tribe Triticeae all of the distant hybridizations using Elymus tsukushiensis and E. ciliaris required embryo rescue because of abortive endosperm. The average of seed set was higher in the cross combination involving the latter species. The rate of germination is different for the two Elymus species. When comparing the results according to the pollen parents, it seens that species specific differences are involved. In the cross combination involving Hordeum vulgare, the hybrid plants showed somatic chromosome instability. So far as examined Elymus species indigenous to Japan hybridized with hexaploid, tetraploid and diploid wheat species using embryo rescue. The F1 hybrids showed almost no chromosome pairing at MI. The general procedure to produce an additional disomic series of the foreign genome chromosomes to wheat is summarized. Results obtained for some E. ciliaris chromosomes are reported.