In this paper, we present design methods for perfect reconstruction (PR) integer-modulated filter banks, including biorthogonal (low-delay) filter banks. Both the prototype filter and the modulation sequences are composed of integers, thus allowing,efficient hardware implementations. To derive such filter banks, we first extend the PR conditions known for cosine modulation to other, more general, modulation schemes. We present solutions where the PR conditions on the prototype and the modulation are entirely decoupled and where some simple coupling is introduced. The conditions are derived for both even and odd numbers of channels. Design examples are presented for both cases.