The present paper is concerned with the global instability mechanisms for the basic steady state of lamellar eutectic growth with curved and tilted interface affected by the triple point. We solve the related linear eigenvalue problem (EVP) by using the analytical approach for the case that the Peclet number is small and the segregation coefficient patametet K is close to the unit. It is found that the system involves two types of global instability mechanisms: the 'exchange of stability' invoked by the non-oscillatory, unstable modes and the global wave instabilities invoked by four types of oscillatory unstable modes, namely (AA)-, (SS)-, (AS)- and (SA)-mode. The quantization conditions for these modes are derived, he neutral curves for these global instabilities on the parameters plane are calculated. The stability criterion yields the range of the interlamellar spacing and explains the interfacial pattern transitions observed in he experiments. (C) 2014 Elsevier B.V. All rights reserved.