In this paper, we investigate serially concatenated continuous phase modulation (SCCPM) with convolutional codes (CC) over rings. The transmitted signals are disturbed by additive white Gaussian noise. The properties for systems with both infinite and finite block lengths are investigated. For an infinite-length system, we check the convergence threshold using the extrinsic information transfer chart. For a finite-length system, we use union-bound techniques to estimate the error floors. In the union-bound analysis, we consider both the order and the position of nonzero permuted symbols. A simple method for determining a CPM error event through the sum of the input symbol sequence is shown. Thus, we can determine if the output symbol sequence of an error event in the ring CC can form an error event in CPM. Two properties concerning the interleaver gain (IG) are investigated. A recursive search algorithm for the maximal IG is shown. Compared with previous SCCPM with a binary CC, the proposed system shows an improvement concerning the convergence threshold or error floors