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We present parallel algorithms for triangular periodic Sylvester-type matrix equations, conceptually being the third step of a periodic Bartels-Stewart-like solution method for general periodic Sylvester-type matrix equations based on variants of the periodic Schur decomposition. The presented algorithms are designed and implemented in the framework of the recently developed HPG library SCASY and are based on explicit blocking, 2-dimensional block cyclic data distribution and a wavefront-like traversal of the right hand side matrices. High performance is obtained by rich usage of level 3 BLAS operations. It is also demonstrated how several important key concepts of SCASY regarding communications and the treatment of quasi-triangular coefficient matrices are generalized to the periodic case. Some experimental results from a distributed memory Linux cluster demonstrate are also presented.