Novel polymers contain phthalocyanine ring systems bonded via axial bonds to a central metal atom in the polymer chain and consist of repeating units of the general formula (I) ##STR1## In the general formula (I), Pc.sup.s is a phthalocyanine ring system having peripheral substituents, Me is the central atom of the phthalocyanine ring system, which atom is bonded in the polymer main chain, suitable central metal atoms Me being silicon and germanium, R is alkylene, R' and R" are each alkyl, cycloalkyl, aryl or alkoxy and Z is a silicon-carbon bond or further Si-containing groups. The novel polymers can be particularly advantageously used for the production of ultrathin layers by the LB technique, optically transparent films having high optical anisotropy and a high volume concentration of phthalocyanine radicals being formed.