A general-order equation-of-motion coupled-cluster (EOM-CC) method, which is capable of computing the excitation energies of molecules at any given pair of orders (m and n) of the cluster operator and the linear excitation operator, is developed by employing a determinantal algorithm. The EOM-CC(m,n) results of the vertical excitation energies are presented for CH+ with m and n varied independently in the range of 1 less than or equal to m,n less than or equal to 4 and for CH2 with 1 less than or equal to m = n less than or equal to 6. EOM-CCSDT [EOM-CC(3,3)] provides the excitation energies that are within 0.1 eV of the full configuration interaction results for dominant double replacement transitions.