Abstract: Bowl-shaped polymer particles characterised by having a bowl-like shape as is formed by partly cutting along a plane each spherical hollow polymer particle having a void in the inside, and in which the cross-section perpendicular to the cut plane and passing through the center of the particle has a shape as is formed by partly cutting a double circle along a straight line, and the lengths H of the perpendiculars from the outer arc of the double circle in the cross-section to the straight line have a maximum value Hmax equal to or larger than the radius of the outer circle of the double circle. The bowl-shaped polymer particles have a multi-layer structure, and are produced by multi-stage polymerization in which monomer mixtures are successively polymerized in a manner such that the proportion of a monomer having an acidic group gradationally decreases and by treating the resultant polymer with a base.

Abstract: A method of producing a polymer of a cationically polymerizable vinyl monomer by polymerizing at least one cationically polymerizable vinyl monomer using a polymerization initiator system composed of an organic compound having a functional group represented by formula (I) below ##STR1## where R.sup.1 represents a hydrogen atom, an alkyl group, or an aryl group; R.sup.2 represents an alkyl group, or an aryl group; X represents a halogen atom, an alkoxy group, or an acyloxy group, and a Lewis acid, wherein polymerization is carried out in the presence of a phosphorus-containing compound selected from the group consisting of a phosphine, a phosphine oxide, a phosphite, and a phosphate.