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A two-dimensional string model with dynamical cancellation of folds is considered. The action of the model contains the self-intersection number which is defined for surfaces immersed into 4D targets. The two additional variables are not dynamical and live on a compact manifold. In this sense the model is a compactification of a 4D theory. The cancellation forces the string $\th$ angle to be equal $\pi$. Candidates for string states are constructed. Some mathematical background is given.doi:10.1142/s0217751x96001280 fatcat:cpz4fja2jvasbkeygscp62gbby