R&D Cooperations among industry, university and research institutes are central parts of National Innovation System. By analyzing the newly collected data (2004)(2005)(2006) from community innovation survey in Taiwan, we explore the determinants for innovative firm to engage in R&D cooperation with five types of partners: competitors, suppliers, customers, universities and research institutes, and identify the correlations (or complementarities) between these five types of R&D cooperation. We find that there is no single determinant has significant impacts on all cooperation types -implying the heterogeneity of the driving forces for different types of R&D cooperation. We also find the inversed-U shape relationship between the R&D intensity and the propensity to cooperate with suppliers, customers and institutions. Therefore, only big firms with modest R&D intensity will vertically cooperate in R&D. The NIS of Taiwan consists of two cores with weakly connections. The first core is R&D cooperations with universities and institutions; the second core is the R&D cooperations within industry (competitors, suppliers, customers). This may indicate the vitality of industrial network of Taiwanese firms, and only part of the industry has close linkages with universities and institutions in Taiwan Innovation System.